Iraq invaded Kuwait in 1990. An international coalition, led by the US, came to Kuwait's aid. None of those countries was in a formal state of war with Iraq -- Kuwait was, and the international troops were just there to help free Kuwait and defend Saudi Arabia.
The shooting stopped due to a cease-fire. There was never a formal peace treaty. If Saddam failed to abide by the terms of the cease-fire, then hostilities would resume. It's a fine distinction, but an important one in the world of international law.
Ergo, the claim that we didn’t need to declare war because the ceasefire was violated doesn’t hold. Iraq was run out of Kuwait - end of “police action”. For a ceasefire violation to warrant toppling a government, when the violation has nothing to do with the act that started the conflict, is an issue of war.