I am actually willing to believe that Congress can declare war without saying "Declaration of War". However, the War Powers Act seems to explicitly recognize the existence of two different things. The very ambiguity which Congress ought to avoid has now been legislated into existence.
Jefferson seems to have conceded that there is a difference between defense and offense. He also seems to have conceded that the actions of the pirates constituted acts of war against the US and not just crimes against persons and property.
He seems to have suggested to Congress that they authorize him to engage in offensive war activities. Jefferson seemed to recognize that Congress has the power to declare war and that he doesn't. Apparently Congress granted Jefferson the use of the military to pursue an achievable objective.
For the life of me, I can't see why there is any reasonable objection to declaring war if one is going to fight a war. Nor can I see any justification for creating an unConstitutional War Powers Act which gives legislative weight to an ambiguity which shouldn't exist.
If our Founders wanted to grant the government the power to conduct law-enforcement in foreign lands, they could have said so. The concept is not so complicated nor so new that it couldn't have been included. Instead, Congress recognized the sovereignty of other nations, expecting them to recognize our sovereignty. The power to declare war is the power to challenge the sovereignty of others. It is only of secondary interest in crime-fighting.
I believe that, in general, a Declaration of War is a superior method of conducting war for many reasons. Primarily, it gives the administration a large and sufficient authority and field of actions; and it imposes upon congress a desire to end the war so they can reclaim the powers they lose to the executive during the duration!