Most of the time I think there's no difference between both of them. But let's say "apetecer" means "to feel like to do something" while "querer" means "to want". So if I ask you "¿te apetece ir al cine?" I would translate it as "would you like to go to the cinema?" and "¿Quieres ir al cine?" -> "Do you want to go to the cinema?". But still, this is not a perfect translation (the first sentence sounds more respectul in English, while it doesn't in Spanish). Even that, I think you can see both mean similar things. "Apetecer hacer algo" means the same as "tener ganas de hacer algo", maybe you know already this expression.
I don't know if I'm clarifying it to you, but I hope you can get my point :) Hope it's helpful :D