"That the state of war between the United States and the Imperial Government of Japan which has thus been thrust upon the United States is hereby formally declared..."
and
"...the state of war between the United States and the Government of Germany which has thus been thrust upon the United States is hereby formally declared..."
For whatever reason, Congress declared in the case of Iraq that
"The President is authorized to use the Armed Forces of the United States as he determines to be necessary and appropriate in order to
"(1) defend the national security of the United States against the continuing threat posed by Iraq; and
"(2) enforce all relevant United Nations Security Council Resolutions regarding Iraq."
Declaring that the President can use the armed forces as he see fits, in my mind, exactly equals, in its effects, declaring the existence of a state of war. The COTUS does not prescribe the language (as it does, for instance, in the POTUS Oath of Office).