It seems like the President has a lot of freedom under the War Powers Act to conduct war without an actual declaration of war. It seems to me that someone could commit treason (as per the Constitution) without a formal declaration of war depending on the definition of enemy. I think the President needs to go back to Congress every 120 when conducting operations under the WPA and I assume this is lifted if war is declared, but I don’t know.
So let’s say the President is conducting military operations under the WPA and Congress declares war … what changes?
A whole raft of statues come into play for one thing. Stuff like aiding and abetting enemies gain real teeth that they don’t really have when it’s a “police action” or something along those lines, for example. I also believe it empowers the Federal government to do things like borrow money to fund the war and to mandate certain things to support the war effort - rationing, production priority, and so forth. There are monster lists of those things in the following links:
The Federation of American Scientists has a paper detailing what changes and how it’s historically done.
It makes it easier to start drafting kids into the armed forces. Not that it prevents it now, just easier from a public perception viewpoint. The Vietnam draft was a disaster from a public viewpoint and is the main reason we have not had a draft since despite numerous conflicts.
There are also laws that come into play to mobilize the economy into fully supporting the war effort. By an official declaration, your economy, the POTUS can direct certain sectors into production of needed material, certain supplys can be restricted and use, rationing can kick in . . . It gives the government a heavy hand in use of an economic engine otherwist left to its own direction.