Yes, but for example, in the U.S. you can get a lot more damages for certain legal concepts which I don't think are present or as well recognized in many European countries. For example, there's the idea of "pain and suffering." So if you're physically harmed by someone, you can claim costs for your hospital stay, damage to your property, missed work, etc, but you can also get an additional sum because of the "pain and suffering" you had to endure.

Oh you mean "damages"? Yes we have that too.