What the difference between non mi piace and non piaccio ??
As far as I am aware (I am not a pro with Italian, although very familiar with it and my other language Spanish has this same rule) "non mi piace" means that you don't like something. For example, "non mi piace la mia vita" = "I don't like my life". "Non piaccio" means that you aren't liked by someone/something. For example, "(Io) non gli piaccio" means "He doesn't like me".
(Io) piaccio = first person singular present tense of piacere, and (lui/lei) piace = third person singular present tense of piacere.
Piacere is an odd verb for English speakers, in that what we think of as the subject is inverted and treated as the indirect object. So:
Mi piace l’uomo = literally “the man is pleasing to me” but since no one says this in English this becomes = “I like the man”
Io non gli piaccio = literally “I am not pleasing to him” = “he doesn’t like me.”
As both LasCicatrices and Dcarl wrote, if you think of the verb in terms of "to be likeable":
non mi piace = (it) is not likeable to me → I don't like it
non piaccio = (I) am not likeable → (others) don't like me.