The two terms are essentially synonymous. "Proselytism /ˈprɒsəlɪˌtɪzəm/ is the act of attempting to convert people to another religion or opinion."
False. Don't use a secular dictionary to define a religious term as used by a religious body.
Here is the definition given by the famous Jesuit priest, Fr. John Hardon, in his Catholic Dictionary:
PROSELYTIZE. Originally to convert someone from one religion to another, either by bringing a person to full acceptance of the new faith and ritual or at least sympathy with it. The more common meaning, however, is to induce people to change their religious affiliation by using unfair and even unscrupulous means. (Etym. Greek proselytos, to convert to Judaism; literally, one who has arrived.)