Proselyte, from Greek προσήλυτος/proselytos, is used in the Septuagint for "stranger", i.e. a newcomer to Israel; a sojourner in the land, and in the New Testament (Strong's G4339 Archived 2009-09-03 at the Wayback Machine) for a convert to Judaism from Paganism. It is a translation of the Hebrew word גר/ger (Strong's H1616 Archived 2009-09-05 at the Wayback Machine).
There are two kinds of proselyte:
A righteous proselyte was a Gentile who had converted to Judaism, was bound to all the doctrines and precepts of the Jewish economy, and was considered a full member of the Jewish people.
A gate proselyte was a "resident alien" who lived in the Land of Israel and followed some of the customs.
The "religious proselytes" spoken of in Early Christian writings were righteous proselytes, as distinguished from gate proselytes.