American cheese is one specific cheese made in America. It's essentially cheese made into a cheese sauce, then chilled back into a block. There's a number of quality levels of it based on how much they skimp on the cheese. And when eaten melted, it's actually pretty decent, if mild.

Most grocery stores in the US have two cheese sections. There's the cheap shredded/sliced cheeses, and then there's a separate section with the fancier cheeses, both foreign and domestic.

Cheese in the US is weird. We make both Velveeta and Humboldt fog. An American cheese won the World Cheese Awards a few years ago, but most of the cheese eaten in America is cheap, mild, mass produced, pre-sliced/shredded semisoft cheese. Most of it isn't "american cheese", though.