A law passed by Congress authorizing acts of war is, ipso facto, a declaration of war (in the sense of an exercise of the Constitutional power to declare war.)

The only effect of not using specific legal phrasing is that it may not trigger other effects under other statutes Congress has passed which require particular language in subsequent law to trigger their effects. This can be important, to be sure, but it doesn't make it any less a declared war.

Open-ended declarations of war are, of course, extremely problematic and open to abuse, which is one of the reasons the last notable one (the Gulf of Tonkin Resolution) was repealed.

I guess we get to learn the lessons of the Vietnam era all over again in this generation. Maybe this time they'll stick...