Whatever they say always appears to be post-hoc rationalization to explain what would otherwise be illegal actions.
They seem to have mostly given up on caring to find such things ahead of time.
(I agree that in practice, a war is a war, whether your nation's laws officially call it as such or not doesn't make much of a difference.)
At least the American public does recognize them as wars, so there's that at least.
I'm not sure this is accurate.
We have plenty of "wars" that aren't wars. Such as the annual "war on Christmas".
Do we recognize them as "wars"? Or do we just use the word?
I say '(mostly)' because while the 'war on Christmas' and WWII are clear cut cases, the war on drugs is an example that sometimes skirts closer to the border. Though it's still very much a metaphorical war.