Convert, proselyte are synonyms only in being applicable to the same person. Both denote a person who has embraced another creed, opinion, or doctrine than the one he has previously accepted or adhered to.
Convert commonly implies a sincere and voluntary change of belief; it is, therefore, the designation preferred by the church, the party, or the school of thought of which such a person becomes a new member.
Convert is also applied to a person who undergoes the religious experience called conversion or a turning from a life of sin or indifference to one guided by religious (specifically, Christian) principles and motives.
Proselyte basically denotes a convert to another religion. It is still used in reference to a convert to Judaism who manifests his sincerity and fidelity by strict adherence to religious laws and practices. In general use, however, the term may suggest less a reverent or convicted and voluntary embracing than a yielding to the persuasions and urgings of another, be it an earnest missionary or zealot or someone with less praiseworthy motives.
Proselyte is often the designation chosen by the members of a church for one formerly of their number who has been converted to another faith. The term is also applied to a person won over to a party, a cause, or a way of life in which he has formerly expressed disbelief or disinterest.