Some research:
A "righteous proselyte" is a gentile who has converted to Judaism, is bound to all the doctrines and precepts of the Jewish economy, and is considered a full member of the Jewish people. They are to be circumcised as adults (different from brit milah) and immersed in a mikvah should they wish to eat of the Passover sacrifice.
A "gate proselyte"[5] is a resident alien who lives in the Land of Israel and follows some of the customs. They are not required to be circumcised nor to comply with the whole of the Torah. They are bound only to conform to the Noahide Laws (do not worship idols, do not blaspheme God's name, do not murder, do not commit fornication (immoral sexual acts), do not steal, do not tear the limb from a living animal, and do not fail to establish rule of law) to be assured of a place in the world to come. - https://en.wikipedia.org/wiki/Proselyte#Two_kinds_of_proselytes_in_Judaism; cf. http://www.biblestudiesonline.info/TGF/topical/proselytes.htm
The term employed generally, though not exclusively, in the Septuagint as a rendering for the Hebrew word "ger," designating a convert from one religion to another. The original meaning of the Hebrew is involved in some doubt...
Whatever may have been the original implication of the Hebrew word, it is certain that Biblical authors refer to proselytes, though describing them in paraphrases. Ex. xii. 48 provides for the proselyte's partaking of the paschal lamb, referring to him as a "ger" that is "circumcised..."
Probably in almost all these passages "converts" are assumed to be residents of Palestine. They are thus "gerim," but circumcised. In the Priestly Code "ger" would seem to have this meaning throughout. In Esther viii. 17 alone the expression "mityahadim" (= "became Jews") occurs...
Ezra's policy, founded on the belief that the new common wealth should be of the holy seed, naturally led to the exclusion of those of foreign origin. Still, the non-Israelite could gain admittance through circumcision (see Ex. xii.)...
There is good ground also for the contention of Grätz (l.c. p. 33) that immediately after the destruction of the Second Temple Judaism made many conquests, especially among Romans of the upper classes. Among the proselytes of this time a certain Judah, an Ammonite, is mentioned. Contrary to the Biblical law prohibiting marriage between Jews and Ammonites, he is allowed to marry a Jewess,..
At this epoch, too, the necessity for determining the status of the "half-converts" grew imperative. By "half-converts" is meant a class of men and women of non-Jewish birth who, forsaking their ancestral pagan and polytheistic religions, embraced monotheism and adopted the fundamental principles of Jewish morality, without, however, submitting to circumcision or observing other ceremonial laws...
Semi-Converts.
In order to find a precedent the Rabbis went so far as to assume that proselytes of this order were recognized in Biblical law, applying to them the term "toshab" ("sojourner," "aborigine," referring to the Canaanites...
According to Simeon b. Eleazar, this form of adoption into Judaism was valid only when the institution of the jubilee also was observed, that is, according to the common understanding of his dictum, during the national existence of Israel ('Ar. 29a). A similar observation of Maimonides ("Yad," Issure Biah, xiv. 7-8; ib. 'Akkum, x. 6) is construed in the same sense. It seems more probable that Maimonides and Simeon ben Eleazar wished to convey the idea that, for their day, the institution of the ger toshab was without practical warrant in the Torah. R. Johanan declares that if after a probation of twelve months the ger toshab did not submit to the rite of circumcision, he was to be regarded as a heathen ('Ab. Zarah 65a; the same period of probation is fixed by Ḥanina bar Ḥama in Yer. Yeb. 8d).
In contradistinction to the ger toshab, the full proselyte was designated as "ger ha-ẓedeḳ," "ger ha-berit" (a sincere and righteous proselyte, one who has submitted to circumcision..
Mode of Reception.
The details of the act of reception seem not to have been settled definitely before the second Christian century. From the law that proselyte and native Israelite should be treated alike (Num. xv. 14 et seq.) the inference was drawn that circumcision, the bath of purification, and sacrifice were prerequisites for conversion...
After the Hadrianic rebellion the following procedure came into use. A complete "court," or "board," of rabbinical authorities was alone made competent to sanction the reception. The candidate was first solemnly admonished to consider the worldly disadvantages and the religious burdens involved in the intended step. He, or she, was asked, "What induces thee to join us? Dost thou not know that, in these days, the Israelites are in trouble, oppressed, despised, and subjected to endless sufferings?" If he replied, "I know it, and I am unworthy to share their glorious lot," he was reminded most impressively that while a heathen he was liable to no penalties for eating fat or desecrating the Sabbath, or for similar trespasses, but as soon as he became a Jew, he must suffer excision for the former, and death by stoning for the latter. On the other hand, the rewards in store for the faithful were also explained to him.
If the applicant remained firm, he was circumcised in the presence of three rabbis, and then led to be baptized; but even while in the bath he was instructed by learned teachers in the graver and the lighter obligations which he was undertaking. After this he was considered a Jew (Yeb. 47a, b).
The presence of three men was required also at the bath of women converts, though due precautions were taken not to affront their modesty. This procedure is obligatory at the present time, according to the rabbinical codes (see Shulḥan 'Aruk, Yoreh De'ah, 268; "Yad," Issure Biah, xiv.). The ceremony should be performed by a properly constituted board of three learned men, and in the daytime; but if only two were present and the ceremony took place at night, it would not therefore be invalid... - www.jewishencyclopedia.com/articles/12391-proselyte
5 Then some of the believers who belonged to the party of the Pharisees stood up and said, “The Gentiles must be circumcised and required to keep the law of Moses.”
OUCH!