~~Go read the text of the 2001 and 2002 AUMFs. It will become clear.~~

Actually, stand by, I'll bring it in again.

September 18th, 2001 AUMF

IN GENERAL.—That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons.

That same day NYT printed an article saying Bush wanted Bin Laden Dead or Alive. So everyone knew exactly which country was being talked about. It was made broad though so AQ couldn't just go hide elsewhere.

October 16th 2002

AUTHORIZATION.—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.

I think that one is pretty self explanatory.