A more recent case which touched on this issue was Hamdan v. Rumsfeld, decided in 2006. There, the plurality opinion noted that their conclusions as to the rights and duties of the parties (i.e. terrorists and the U.S. government) did not rely on whether a formal declaration of war was issued. It was enough that a state of war existed to trigger the safeguards of law.
Second, lets see what Congress has had to say about it, or rather one Congressman in particular. Senator Joe Biden, responding to questions from reporters shortly after voting for the AUMF 2001 said:
M: (Inaudible) Talbot(?). Senator, thank you for this broad gauged approach to the problems we face. My question is this, do you foresee the need or the expectation of a Congressional declaration of war, which the Constitution calls for, and if so, against whom? (Scattered Laughter)
JB: The answer is yes, and we did it. I happen to be a professor of Constitutional law. Im the guy that drafted the Use of Force proposal that we passed. It was in conflict between the President and the House. I was the guy who finally drafted what we did pass. Under the Constitution, there is simply no distinction
Louis Fisher(?) and others can tell you, there is no distinction between a formal declaration of war, and an authorization of use of force. There is none for Constitutional purposes. None whatsoever. And we defined in that Use of Force Act that we passed, what
against whom we were moving, and what authority was granted to the President.