They aren't the same thing at all. We've had Presidents ask for authorization
without asking for a declaration since the 18th century - the Quasi War was the first I believe.
The precedent is well understood. The President may ask for authorization for any extended war and for a formal declaration, if desired. Then, and only then, will Congress act. Congress will not issue a declaration absent being asked by Commander of the military, for obvious reasons.
This idea that Congress is somehow not doing its job because it's not issuing a formal declaration that were not requested nor required, is simply nonsense.
Frankly, if requesting authorization was the same thing as requesting a declaration, then one could just as easily argue Congressional approval of funding for a war is a declaration.