The Founders were not unanimous in their thinking. The words describe specific ideas which are to be interpreted for their meaning by taking into account the thinking of the Founders. I don't think that is the same thing. The fact that Jefferson, Adams, or any other President may have violated the Constitution wouldn't change what our Founders accomplished.
I haven't looked up a complete source of the War Powers Act but the snippets offered by others indicate that the law makes a clear differentiation:
Notwithstanding subsection (b), at any time that United States Armed Forces are engaged in hostilities outside the territory of the United States, its possessions and territories without a declaration of war or specific statutory authorization, such forces shall be removed by the President if the Congress so directs by concurrent resolution.
This appears to indicate that a "declaration of war" is not the same as a "specific statutory authorization".
These are the word chosen by Congress to exercise its powers under the Constitution.
Of course not, yet obviously (since it is specifically mentioned) the congress that wrote this believed "specific statutory authorization" is a Constitutional means of conducting war.
As Adams and Jefferson believed.
William Tell said: "The Congress is obligated to declare war if they believe that the President is justified in carrying out a war against an enemy. That is their duty. "
I hope you see that this just ain't so, and I suggest that you would do better to believe because Jefferson and Adams- and their congresses- did, than because some later congress did!
Later congresses have said some very iffy things about the constitution!