Crave is a bit stronger. To crave is to feel a powerful/intense desire.

'crave' has several meanings... 1) to long for; want greatly; desire eagerly 2) to require; need 3) to ask earnestly for (something); beg for 4) to ask (a person) earnestly for something or to do something.5) to beg or plead 'desire' also has several meanings... 1) to wish or long for; crave; want 2) to express a wish to obtain; ask for; request 3)a longing or craving, as for something that brings satisfaction or enjoyment 4) an expressed wish; request 5) sexual appetite or a sexual urge. These two can be partially interchangeable, but as you can see by their definitions, be careful how each word is used. I hope this answers your questions. ~Samantha :)