Joe, for the most part the letter after a model number does not indicate anything specific--other than the factory that it came out of. In this case, "M" for "Monza." So it's entirely possible the Monza factory also made aluminum 306s, which would still be badged as 306M's.
If you do a Google Image search for "Singer 306" you'll see what they look like. The body is the same as the 319, but without the "typewriter" keys at the back.