Maybe there's more Mexican food in your area, since Mexico has used "manchego" for a while to refer to a kind of cow's milk cheese.

In Mexico manchego is a very specific cheese and definitively not used to define generic cow cheese.

It's a specific cheese, but I think it's the one that the original commenter is seeing - it tastes much more "normal" to Americans than Spanish manchego, and I've never seen the label on anything other than the two kinds.

A very specific variety of the most genericized melting cheese in the entire country which isn’t even kind of close to queso manchego in Spain, but the previous commenter already mentioned it was “a specific kind” of cheese anyways.