A lot of the places by me have both a Chinese menu and a Japanese menu. Some even have a Thai menu.
So when you're going out for Asian food, it really is that. No sense in being pedantic here.
I went to a combo thai-chinese place once... Now I want sesame chicken...
And I doubt the contents of any of those menus are particularly close to what you'd find in the countries they claim to be from. It's really more like "Asian-inspired."