The President of the United States, qua president, has the power to sign Congressional declarations of war. The President of the United States, qua private citizen, has no power to sign Congressional bills of any kind.
Qua
Definition
Acting in the capacity of. After identifying a person, the word "qua" may be added to signify that the rest of the statement pertains to that person acting in the capacity of whatever title or position comes after "qua."
Illustrative caselaw
See, e.g. New Jersey v. Delaware, 552 U.S. 597, 600 (2008).
See also