I agree with gasman, to declare war is to make a formal statement that your state is, from that moment on, at war with another. You can wage war without declaring it, and I think that is implied in my example from the US Constitution.
Here is a great example from the OED which makes this clear that war is levied without being declared:
"The Syrian King [...] Assassin-like had levied Warr, Warr unproclam'd."