In this case, it's the Constitution that contains those words requiring precise meaning because it's our contract with the federal government.
If "Authorization for the Use of Military Force" ≡ "Declaration of War", then why has Congress not used the words "Declaration of War" since 1941?
That is an important question that requires an answer. It is at the crux of the debate.
Your refusal to answer questions paints a vivid picture of your debate failure. You might want to put some effort into exploring this question and its real answer. (Hint: The answer is really quite simple and if you spend a little time re-examining the equation, you'll see it clearly.)
BTW, "military force ≠ mopping floors" is irrelevant to the answer.