The two words can usually point to the same action——to kiss (maybe 吻 sounds more decent and formal sometimes, but 亲 is a good word, too, no problem). I think the difference comes mostly from the origin meaning of the two characters: 亲 refers to an emotional intimacy towards someone, this feature can also be felt in the verb 亲;吻 as a noun means mouth(aligators are called 短吻鳄 in Chinese), so when it becomes a verb, it points more to an action performed by one's mouth.