I think they are confusing no matter what you call them.Indian Game, are just now mainly called Cornish Games, or Just Cornish nowadays.
Think that's where the confusion came from when you just said Indian Gamefowl.
If you say "Cornish," then people assume you mean the big white Cornish Cross meat birds.
If you say "Cornish Game," some people are going to think of those little chickens you can buy in the grocery store (Cornish Cross butchered young).
And as you pointed out, "Indian Game" or "Indian Gamefowl" causes another kind of confustion.
I personally like Cornish (pure breed, standard or bantam, also called "Indian Game" and various other names). But I think they do have too many names, and every one of their names is easy to confuse with something else!