Something like is going on between Russia and Ukraine, Israel and Iran (borderline). The Iraq war. The Afghanistan war. A prolonged period of hostilities.
Something you would look back at and call "The US Iran War". I don't think the previous acts of violence, or the current one, between these two meets the mark yet. And it's not clear if this one will. Iran can't really do much right now and it's not clear whether the US will go a lot further here.
E.g. we probably aren't going to look back at the hostilities with Yemen and call them the "US-Yemen war" or the "US Houthis war" like we look at Vietnam, Korea, Afghanistan, Iraq.
Or as Putin would put it, it's a special military operation (yeah yeah, that one is a war).
The US has had many bombings of other countries without a full out war:
https://www.maurer.ca/USBombing.html
Most recent big example is Yemen. Would you say the US is at war right now with Yemen?
Was this already the start of this war? https://en.wikipedia.org/wiki/Operation_Praying_Mantis
I guess you could say that during the bombing campaign in Yemen until the ceasefire (and maybe now) they were at "war".
Were Israel and Iran "at war" when they exchanged blows a year ago?