Generally, "wants" refers to what the character is trying to achieve on the surface, in the short term, while "needs" refers to the bigger life lesson that the character needs to learn to be happy - or sometimes it's the character flaw he or she needs to work on. (In movies especially, this is often referred to as the arc.) For example, in FORGETTING SARAH MARSHALL, Peter WANTS to get Sarah back but NEEDS to move on and focus on getting his life and career together. In VERONICA MARS, Veronica WANTS to solve the case of the week (or season), but she NEEDS to learn to trust and forgive people. (Apparently I've got Kristen Bell on the brain.)
Ideally, the more stuff like this you figure out before you start writing, the fewer soul-crushing rewrites you'll have to do later!