A béchamel sauce is made from butter, flour made into a roux, with milk added.
If you add cheese to a béchamel sauce it's a "child" sauce called mornay.
If you make it with chicken stock instead of milk it's a veloute sauce, another momma sauce.
Only cheese sauces made from béchamel are rightfully called mornay. I make my Mac and Cheese using a mornay sauce.
James Peterson has written a great book on sauces
Less is not more. More is more and more is fabulous.