That's a difference without a distinction. Getting Congressional permission to send in armed forces is "declaring war", regardless of what the resolution calls it. The point of that clause in the Constitution is for Congress to provide the necessary check and balance on presidential use of military force.
We'll agree to disagree but I think we can both agree that "declaring war" seems to be an optional thing for Presidents, and as such, is possibly the most pointless part of the Constitution.
Only way I could see it having teeth is if the opposite happened (Congress wanted to declare war but the President didn't).