I am in agreement. proselytizing Vs evangelism. Conversion is the movement from nonbeliever(atheist, Buddhist , Hindu. Muslim) to believer to any of the faith groups. Movement from one to the other and especially active recruitment to me is proselytizing
Some “Born Again Christians” don’t consider Mormons, Quakers, Unitarians, Catholics, Jehovah’s Witnesses, to be Christians. Probably a few others as well.