The word Guer (גר) in the Torah has several meanings. It is usually identified with only one of them in the texts, but, in practice, in each of the texts it has a specific meaning and, must be interpreted according to the context (Talmud Chullin 115b, Braita of Rabbi Ishmael in Torat Cohanim beginning of Vayikra).
The very root of the word is from the verb lagur (לגור) means "to live," "to inhabit." See Rashi on Exodus 22:21: "Every word גר signifies a person who was not born in that country but came from another country to live there.".
Stranger/Outsider
The first meaning we find in the Torah is "stranger," as in Genesis 23:4, when Abraham wants to buy a plot of land to bury Sarah: "I am a stranger and a sojourner among you." Clearly, Abraham is expressing that he does not belong to the people of the Benekhyun from whom he wanted to buy the land, etc.
Convert
A convert is a person who was not born Jewish (that is, not born to a Jewish mother) who joined the Jewish people through the process of conversion. Such a person has the same laws as a Jew by birth, as expressed in Leviticus 19:34, "The convert who lives among you will be treated as one of your own." It is interesting to note in this same verse that Guer It means convert and "that he may dwell with you" is written HaGar, I mean, ""HaGuer HaGar"" (הַגֵּר הַגָּר)... same letters with different vocalizations.
Another example is Deuteronomy 10:19: "They will love the one who has turned back, for they were strangers in the land of Egypt." The translation of HaGuer (הַגֵּר) as "convert" and Gerim (גֵרִים) as "strangers" is not whimsical, Onkelus and Rabbi Jonathan ben Uziel say so in their translations (וְתִרְחֲמוּן יָת גִּיּוֹרָא אֲרֵי דַּיָּירִין הֲוֵיתוֹן בְּאַרְעָא דְּמִצְרָיִם).
We find the same in Exodus 22:20: "Do not deceive a convert... for they were strangers in the land of Egypt." It is interesting to note that Ramban explains the connection between "convert" and "stranger," saying that you might think the convert has no one to care for him because he comes from a different people, etc., but you should know that just as I (says God) saved you from the suffering of Egypt, where you were a stranger and had no one to help you, in the same way I will help the convert...
Stranger (Guer toshav)
In other words, a foreigner living in the Land of Israel but not converted to Judaism. He simply agreed before a rabbinical court to fulfill the seven commandments of Bnei Noach. We are permitted to let him live in our land. These laws only apply when the entire Jewish people live in the Land of Israel, we have a king, etc., conditions that do not apply today. This is found in Talmud Avodah Zara 64b.
Example: Deuteronomy 14:21: "Do not eat the flesh of dead animals (nevelá - נְבֵלָה), to the stranger (Guer "You must give it to him at your gates." If this were a convert (to whom all the laws of Judaism apply, just like a Jew born of a Jewish womb), why would he be able to eat something that is forbidden to a Jew? Then, clearly, he is talking about a Ger Toshav.
Gentile
Guer No It generally means gentle (as opposed to Ger Toshav).
The Gentile in the Torah is known as Nochri (נָּכְרִי), as in Deuteronomy 23:21: "You shall charge interest to the Gentile, but not to your brother." Clearly distinguishing the Gentile from the Jew, your brother.
Or in Deuteronomy 17:15: "You may not set a foreigner over you," which refers to a Gentile as king of the Jewish people. In this last verse, the difference between "You must set a king..." is also clear. from among your brothers .You cannot place above yourself a strange man"
It is interesting to note that the same word is used in other contexts, even indicating a Jew, as in Shmot 21:8: "To a foreign people," where it means that the father cannot sell his daughter a second time.