There are five mother sauces, Bechemel, Veloute', Espagnagnole(Brown Sauce) , Hollandaise and tomato sauce, though some would replace the Tomato Sauce with Vinaigrette.
Bechemel: Traditionally, Bechemel sauce was made with a thick veal stock. Today, it's usually made with a white roux and milk or cream, with a bit of salt and nutmeg.
From it, small, or derivative sauces are made, such as Alfredo - Bechemel with Parmesano Regiano (though many make this sauce simply with heavy cream and Parmesan Regiano), Mornay - Bechemel with Guyere, and others. The following URL shows a few of the many derivative sauces made from Bechemel: RecipeSource: Bechamel Sauce
Veloute is also made with a white roux, though I cook to the blonde stage (very lightly browned), then combined with veal, poultry, or pork stock or broth (in the U.S., this is simply known as a flour based gravy). Here is a site that gives a little more information: What is Velouté Sauce?
And so it is with the other mother sauces. They are not usually used by themselves, but are the mothers, from which other sauces, called daughter, small, or derivative, sauces are made. A few exceptions would be sausage gravy, which if you think about it, is a sausage grease Bechemel to which browned sausage is added. Creamed chipped beef is Bechemel with dried chip beef is re-hydrated and served in. Chicken Ala King is Bechemel with veggies and cooked chicken meat added. And so it is with creamed veggies.
Another cheese sauce that can be made with Bechemel is Cheddar Sauce, usually made by adding a bit of yellow, prepared mustard, and grated sharp cheddar cheese, with the Bechemel removed from the heat.
The technique is very simple. Simply combine equal parts fat and flour over medium heat and stir until combined. Add a bit of salt, and nutmeg and stir while slowly adding milk or cream. The sauce with at first begin to clump, and then turn into a thick paste. As more milk or cream is whisked in, it will start to loosen up and become very creamy smooth. Continue adding liquid until a velvet-smooth sauce is formed. Remove from the heat and add whatever cheese or other ingredients is required to make the kind of sauce you want. The cheese should be grated and at room temperature so that it will complete melt and combine with the Bechemel sauce. The strength of the cheese flavor depends on how much, and how strong the cheese is.
Veloute can be made from the broth from split-pea soup, before the soup is cooked down to the thickened stage. This will temper the strong flavor of the pea broth when the Veloute is added back into the soup. This is called binding the soup, and will keep pea solids from sinking to the bottom of the pot, or suspend the solids. It isn't required for pea soup, and many opt to thicken the soup by simply boiling it down until the split-peas dissolve and naturally suspend themselves. Which version you like best is completely up to you.
So, as you can see, Bechemel is much more than simply a "white sauce". It is the mother from which a myriad of small sauces are built.
Seeeeeeya; Chief Longwind of the North