What are the similarities of contemporary and classical ballet?

The fundamental: Ballet training. All leg and arm positions are basically the same, with any performance it is perfectly acceptable in both branches of ballet to "cheat" and stylize the details (like angle of hands or head) a bit. In Classical, however, there are limits to how much one can do. For example, rarely in a Classical ballet class do they ask you to work with parallel legs: they must always be turned out. Additionally, costumes and music are usually classical as well. Costume is pink tights, and some form of tutu, at least. Contemporary ballet is easier to define. It might, choreographically, appear to be a mixture of modern or lyrical dance and ballet. Costuming and music doesn't have to be classical either. It's really quite supportive of experements.