If you say that there is a curse on someone, you mean that there seems to be a supernatural power causing unpleasant things to happen to them.
(对某人的) 诅咒 He shot her an angry look and a curse. 他投给她愤怒的一瞥和一句诅咒。
If you curse someone, you say insulting things to them because you are angry with them.
咒骂 (某人) I cursed and hobbled to my feet. 我诅咒着,蹒跚着站起来。