Are Wars, with no home soil involvement, actually just good for inflation but not growth?

I grew up, being taught that WW2 was extremely profitable to the American Economy. Which may have been true seeing as Europe was buying a bunch of our goods in the aftermath.

However, I am observing the War in Ukraine, which seems to be really good at driving up global inflation.

Despite sending supplies to Ukraine, it doesnt seem that the military spending is a huge boom for the American economy.

We are getting hit with all that inflation though.

Are Wars actually bad at contributing to real economic growth but "good" at contributing to inflation?