Hey Breezy, before I was "brainwashed" at culinary school, I called it white sauce too. And that's how I think of it, but for some reason that word pops out of my mouth!
As for mornay, if you want to get technical, which my french instructor always did, it is ONLY Mornay if you use a standard bechamel and add only gruyere to it. Buy ya, when all is said and done it is ALL just cheese sauce no matter the base sauce or type of cheese.
By the way I am getting defensive, just making fun of myself and my own schooling!