Proselytism relies on force. Evangelism relies on love. Proselytism is bad news. Evangelism is Good News. Proselytism applies the whip.
Evangelism holds forth the carrot.
There is all the world of difference between them. They were in competition to see who was stronger. They decided to try out their powers on a man walking down the road. The North Wind blew and blew and blew - and the freezing cold only served to make the man draw his cloak more tightly around him. The Sun shone, and before long the heat was such that the man threw off his cloak.