Loving the "Ger"
The Bible is concerned with relations with those who are living within the Israelite community whether with

  • other Israelites ("love your neighbor as yourself" ואהבת לרעך כמוך) or
  • with the "ger," long-term foreigners who are living within the Israelite community ("love the ger" ואהבתם את הגר).
However, according to Maimonides, the commandment to love the "ger" refers to our obligation to converts. The question is: Does the commandment to love one's neighbor include the convert? If so, then it would seem that "love the convert" is redundant.
Is it redundant or does the commandment require something special? If the latter, then how should we understand the mitzvah ואהבתם את הגר?

מִצְוָה עַל כָּל אָדָם לֶאֱהֹב אֶת כָּל אֶחָד וְאֶחָד מִיִּשְׂרָאֵל כְּגוּפוֹ שֶׁנֶּאֱמַר (ויקרא יט יח) "וְאָהַבְתָּ לְרֵעֲךָ כָּמוֹךָ". לְפִיכָךְ צָרִיךְ לְסַפֵּר בְּשִׁבְחוֹ וְלָחוּס עַל מָמוֹנוֹ כַּאֲשֶׁר הוּא חָס עַל מָמוֹן עַצְמוֹ וְרוֹצֶה בִּכְבוֹד עַצְמוֹ. וְהַמִּתְכַּבֵּד בִּקְלוֹן חֲבֵרוֹ אֵין לוֹ חֵלֶק לָעוֹלָם הַבָּא:

אַהֲבַת הַגֵּר שֶׁבָּא וְנִכְנָס תַּחַת כַּנְפֵי הַשְּׁכִינָה שְׁתֵּי מִצְוֹת עֲשֵׂה. אַחַת מִפְּנֵי שֶׁהוּא בִּכְלַל רֵעִים וְאַחַת מִפְּנֵי שֶׁהוּא גֵּר וְהַתּוֹרָה אָמְרָה (דברים י יט) "וַאֲהַבְתֶּם אֶת הַגֵּר".

צִוָּה עַל אַהֲבַת הַגֵּר כְּמוֹ שֶׁצִּוָּה עַל אַהֲבַת עַצְמוֹ שֶׁנֶּאֱמַר (דברים ו ה) "וְאָהַבְתָּ אֵת ה' אֱלֹהֶיךָ".

הַקָּדוֹשׁ בָּרוּךְ הוּא עַצְמוֹ אוֹהֵב גֵּרִים שֶׁנֶּאֱמַר (דברים י יח) "וְאֹהֵב גֵּר":

It is mandatory upon every man to love each and every one of Israel even as he loves his own self, for it is said: "But thou shalt love thy neighbor as thyself" (Lev. 19.19.). One is therefore, obliged to speak in praise of his neighbor, and to be considerate of his money, even as he is considerate of his own money, or desires to preserve his own honor. "But whosoever glorifies himself in disgracing his neighbor has no share in the world to come" (Yerushalmi, Hegigah. 2.1). The love for the proselyte, who came and embraced the protection beneath the wings of the Shekinah, rests upon two mandatory commandments, one because he is included in the commandment concerning a neighbor, and the other because he is a stranger, and the Torah charged us, saying: "Love ye therefore the stranger" (Deut. 10.19.). He commanded on the love for the stranger as He commanded concerning the love for Himself, saying: "And thou shalt love the Lord thy God" (Ibid. 6.5.). The Holy One, blessed is He! loves the strangers Himself, even as it is said: "And (He) loveth the stranger" (Ibid. 10.18).

Rambam
Rambam seems to make several points.
First, the "ger" is someone who has finished the conversion process. (Had Rambam said that the "ger" is in the process of conversion, then there would be no redundancy. "Love your neighbor" applies to Jews including converted Jews, and "love the ger" refers to the person undergoing conversion.)
Second, given that Rambam defines the "ger" as someone who has converted. He provides two reasons for the additional commandment to love the "ger" even though the convert would be included in the commandment "love your neighbor as yourself."
#1. Loving your neighbor does not mean one must actually love one's neighbor. Rather, it means we must act in a particularly way, namely, we must treat our neighbor as we would want to be treated. However, loving the "ger" is not just about treating the convert nicely. It's about feeling something: admiration, respect, affection, and appreciation for someone who has rejected another religion and embraced our God, our values, our culture, our religion, our people. This grand commitment should engender not just good action but a profound emotion.
#2. God loves the "ger" (after all, the stranger loves God; it's reciprocal). We should share in God's ultimate concerns and loves. Therefore, love of the "ger" is an extension of our love of God. We should love those whom God explicitly loves.
Notice that Rambam does not say "love the ger because you were gerim in Egypt." Nowhere is our experience mentioned in conjunction with the mitzvah to love the "ger." It's worth thinking why Rambam omitted this rather obvious justification for the commandment. Or, to ask the question differently, if the "ger" is a convert, according to the Rambam, how does he understand the verses in the Torah that say "love the ger because you were gerim in Egypt?"
The Sefer HaChinuch
The author of the Sefer HaChinuch seems to go in a slightly different direction. He says that the commandment to love the convert is not an injunction to love the convert more than we love the born Jew. It is not a commandment to feel affection and admiration towards the convert in a way that we are not obligated to do so with the native born Jew.
Rather, it is much simpler. We are required to love the convert as much as we love the born Jew. Sefer HaChinuch seems to make the perceptive observation that, left on our own, we are not so welcoming to those who are different from us. Converts come from a different culture and family, not just different religion. They have given up all that because they have seen the truth in Judaism, and they have done so without a support network.
Sefer HaChinuch says that we born Jews tend to be cliquey or a bit xenophobic, and "love the convert" means at the very least to treat the convert as we treat our fellow Jew who was born Jewish. We should love the convert the same, not more than the born Jew, but there is added urgency because converts need support having cut themselves off from their past and all that is familiar to them.

מצות אהבת הגרים - שנצטוינו לאהב הגרים, כלומר, שנזהר שלא לצער אותם, בשום דבר, אבל נעשה להם טובה ונגמל אותם חסד כפי הראוי והיכלת, והגרים הם, כל מי שנתחבר אלינו משאר האמות שהניח דתו ונכנס בדתנו, ועליהם נאמר (דברים י יט) ואהבתם את הגר וגו'.

ואף על פי שיכללהו כמו כן הצווי בישראל, שנאמר עליו "ואהבת לרעך כמוך", שהרי גר צדק בכלל "רעך" הוא, הוסיף לנו השם בו מצוה מיוחדת לו באהבתו, וכמו כן הדבר במניעה מלרמות אותו, שאף על פי שהיה בכלל "ולא תונו איש את עמיתו" (מצוה שלח), הוסיף לנו הכתוב בו מניעה מיחדת לו, באמרו "וגר לא תונה" (מצוה כג).

...משרשי המצוה. כי השם בחר בישראל להיות לו לעם קדוש ורצה לזכותם, ולכן הדריכם וצום על דרכי החנינה והחמלה, והזהירם להתעטר בכל מדה חמודה ויקרה למצא חן בעיני כל רואיהם, ויאמרו (יחזקאל לו כ) ״עם יי אלה״.

וכמה היא דרך נעימות וחמדה להתחסד ולגמל טובה לאשר הניח אומתו וכל משפחת בית אביו ואמו, ויבוא לחסות תחת כנפי אומה אחרת באהבתו אותה, ובבחירתו באמת ושנאת השקר.... מדיני המצוה. מה שאמרו זכרונם לברכה (ב''מ נח, ב) שלא יאמר אדם לגר זכור מעשיך הראשונים....וכל זה שלא לצערו בשום ענין.

והפלגת האהבה שהפליגו בהם עד שאמרו, שהשוה הכתוב אהבתם לאהבת המקום, שבהם נאמר ״ואהבתם את הגר״, ובאהבת המקום ״ואהבת את ה׳ אלהיך״.

ונוהגת מצוה זו בכל מקום ובכל זמן בזכרים ונקבות. והעובר עליה ומצער אותם, או שמתרשל בהצלתם, או בהצלת ממונם, או שמקל בכבודם מצד שהם גרים ואין להם עוזר באמה, בטל עשה זה. וענשו גדול מאד, שהרי בכמה מקומות הזהירה תורה עליהם.

The commandment of loving the strangers (converts): That we were commanded to love the converts, meaning to say that we be careful not to cause them pain in any thing, but [rather to] do them good and grant them kindness according to what is proper and is possible. And converts are anyone who connects with us from the other nations, that leaves his religion and enters into our religion. And about them is it stated (Deuteronomy 10:19), "And you shall love the stranger, etc." And even though the commandment (Sefer HaChinukh 243) about the Israelite includes him, as it is stated about him (Leviticus 19:18), "and you shall love your neighbor as yourself" - since behold, a righteous convert is included in "your neighbor" - God added for us a specific commandment about his love. And so too is the thing in the prevention against cheating him. As even though he was included in "A man shall not wrong his countryman" (Leviticus 25:17, Sefer HaChinukh 338), Scripture added a specific prevention about him in its stating, "You shall not wrong a stranger" (Exodus 22:20, Sefer HaChinukh 23). And they said in the Gemara (Bava Metzia 59b) that one who wrongs the convert transgresses because of "[A man] shall not wrong" and because of "You shall not wrong a stranger." And so too [with this], he nullifies the commandment of "and you shall love your neighbor" and the commandment of "And you shall love the stranger."
Sefer HaChinuch concludes by making a comment not just about converts but about anyone who leaves behind his/her past or family or hometown and moves into a new community. We tend not to treat outsiders as we would want to be treated (love your neigbhor as yourself), yet newcomers to one's community are precisely the people who most need our support. The commandment to love the "ger" reminds us to leave our zone of comfort and reach out to the strangers in our midst and provide them the social network they need to thrive.

ויש לנו ללמד מן המצוה היקרה הזאת לרחם על אדם שהוא בעיר שאינה ארץ מולדתו ומקום משפחות אבותיו, ולא נעביר עליו הדרך במוצאנו אותו יחידי ורחקו מעליו עוזריו, כמו שאנו רואים שהתורה תזהירנו לרחם על כל מי שצריך עזר, ועם המדות הללו נזכה להיות מרחמים מהשם יתברך, וברכות שמים ינוחו על ראשינו, והכתוב רמז טעם הצווי באמרו כי גרים הייתם בארץ מצרים, הזכיר לנו שכבר נכוינו בצער הגדול הזה שיש לכל איש הרואה את עצמו בתוך אנשים זרים ובארץ נכריה, ובזכרנו גדל דאגת הלב שיש בדבר, וכי כבר עבר עלינו, והשם בחסדיו הוציאנו משם יכמרו רחמינו על כל אדם שהוא כן.

(1) The commandment of loving the strangers (converts): That we were commanded to love the converts, meaning to say that we be careful not to cause them pain in any thing, but [rather to] do them good and grant them kindness according to what is proper and is possible. And converts are anyone who connects with us from the other nations, that leaves his religion and enters into our religion. And about them is it stated (Deuteronomy 10:19), "And you shall love the stranger, etc." And even though the commandment (Sefer HaChinukh 243) about the Israelite includes him, as it is stated about him (Leviticus 19:18), "and you shall love your neighbor as yourself" - since behold, a righteous convert is included in "your neighbor" - God added for us a specific commandment about his love. And so too is the thing in the prevention against cheating him. As even though he was included in "A man shall not wrong his countryman" (Leviticus 25:17, Sefer HaChinukh 338), Scripture added a specific prevention about him in its stating, "You shall not wrong a stranger" (Exodus 22:20, Sefer HaChinukh 23). And they said in the Gemara (Bava Metzia 59b) that one who wrongs the convert transgresses because of "[A man] shall not wrong" and because of "You shall not wrong a stranger." And so too [with this], he nullifies the commandment of "and you shall love your neighbor" and the commandment of "And you shall love the stranger."

(2) It is from the roots of the commandment that God chose Israel to be a holy nation and wanted to give them merit. And therefore He guided them and commanded them about the ways of grace and compassion and warned them to crown themselves with every beautiful and precious trait to find grace in the eyes of all who see them, [such] that they will say, "These are the people of the Lord" (Ezekiel 36:20). And it is so much the way of pleasantnesses and beauty to show kindness and to grant good to one who leaves his people and all the family of the house of his father and mother and comes to take shelter under the wings of a different nation in his love for it, and in his choosing of truth and his hatred for falsehood. And in our meriting these good traits, the goodness of God will rest upon us and cling to us, and nothing will prevent us from it; as the good will extend to the good ones and the opposite to the bad ones.

(3) From the laws of the commandment - that which they, may their memory be blessed, said (Bava Metzia 58b) that a person not say to a convert, "Remember your early deeds"; that which they said (Sanhedrin 94a), that a person not disgrace an 'Aramean' in the presence of a convert until the tenth generation, and all of this is not to cause him pain in any regard; the intensification of love that they focused upon them to the point that they said that Scripture equated their love with the love of the Omnipresent, as with them it states, "And you shall love," and with the love of the Omnipresent, "And you shall love, etc.," and that is as I have written in the Order of Mishpatim about the commandment to not oppress the convert, even with words (Sefer HaChinukh 63); and the rest of its details - are in the Midrash and in [various] places in the Gemara (see Mishneh Torah, Laws of Human Dispositions 6).

(4) And this commandment is practiced in every place and at all times by males and females. And one who transgresses it and causes them pain or is negligent in saving them or saving their money, or treats their honor lightly due to their being converts and not having a helper in the nation, has violated this positive commandment; and his punishment is very great, as behold, the Torah has warned about them in several places. And we should learn from this precious commandment to have mercy on a man who is in a city that is not the land of his birth and the place of the family of his fathers. And we should not pass him by on the road when we find him alone and that his helpers are far from him, since we find that the Torah warns us to have mercy on anyone who needs help. And with these traits, we will merit to receive mercy from God, may He be blessed, and the blessings of Heaven will rest upon our heads. And Scripture hints to the reason of the command when it states, "since you were strangers in the Land of Egypt": It mentions to us that we were previously burnt by this great pain that there is to every man who sees himself among foreign people and in a foreign land. And upon our remembering the great worry of the heart that there is in the matter, and that it already passed over us and that God, in His kindnesses, took us out of there, our mercies for any person like this will overwhelm [us].