Public opinion in 2001 and 2003 followed the 9/11 terror attack and was very fresh in peoples mind. A more recent war (2015) would be the attack on Yemen by Barack Obama.
I can however not find any good public opinion for that war.
We've been bombing Yemen on and off since post 9/11, including a rather large attack with UK support just last year (2025). Are you thinking of the Saudi-led intervention that occurred in 2015 in Yemen as part of the Yemeni civil war? Or maybe when we built a base there in 2011 to facilitate more drones?
I don't think Americans perceive much of a difference between attacking Al Qaeda++ in Afghanistan versus in Yemen, certainly not enough to see it as "a different war", and it's not clear that perception is incorrect.