As I mentioned in my other comment, I assumed they were the same, but several sites said they were different things. "American coffee" is a weak brewed coffee, and Caffe Americano (アメリカノ) is a diluted espresso, which is actually stronger than most brewed coffees, at least in terms of caffeine content. Japan has アメリカノ too, and in my experience it's much more common.
I thought maybe it was supposed to say Americano, but it's not the same. There's an explanation here. It's made from light roasted beans, and they say it most likely got it's name from Americans in post-war Japan brewing coffee with lots of water or diluting it further before drinking.
I'm not American, but the name sounds a little judgemental to me.
There seem to be multiple Japanese names for things that are tied to some other nationality with unclear logic.
I'll never forget being at the train station in Kawaguchiko and seeing a フランスドッグ (France Dog) on the menu. It was a hot dog on a stick inside of batter (like a corndog), but with cheese also inside the batter layer.