There isn't a word for ”爱喜“. I speculate that you are talking about ”喜爱“。The meaning of "喜爱” is to be fond of or to like.
喜爱+某物 【correct，written language】 eg. 喜爱电影/健身
喜爱+某人【wrong】 you have to use "喜欢" in this case.
As to difference between "喜欢“ and "爱”，I omit the things we all know, just want to talk about one thing:
In the States, say some guys run into a pretty girl in a coffee shop, one is attracted to her, the others may say that the one loves her, They only mean he is attracted and likes her rather than the "love love" thing. In China, we only use 喜欢 on this occasion.