There are many debates about this terminology but it is safe to assume that a "machine gun", as such, is crew served and can and does fire rifle caliber ammunition fully automatically by holding the trigger. A sub-machine gun doesn't need a crew. A machine pistol is hand held, no shoulder mount. And a so-called assault rifle is "sub-caliber" only to the extent that it's caliber is not a large, long range caliber - it is not defined as having pistol caliber cartridges. That is an error. See below.
The ATF and the public do not always understand these distinctions.
The online dictionary definition of an "assault weapon" is "any of various automatic and semiautomatic military firearms utilizing an intermediate-power cartridge, designed for individual use". That is, however, a political statement because a semi-automatic firearm is never an assault weapon. An assault rifle or "weapon", if you will, is always fully automatic, select fire or not, namely, a hand held machine gun.
Not to belabor the point, but I must - the Germans introduced this terminology in WW2 with their Sturmgewehr 44. A "gewehr" is a rifle in German. As you might imagine, German being a colorful language in many respects, "sturm" translates to storm in English and the point was that firing this fully automatic rifle raised up a storm of bullets, a hail of bullets being a more accurate term in re the weather analogy.
Understand that the Schmeisser (named for the inventor) or Stg44 was literally the first successful assault rifle. It used what is called an "intermediate cartridge", currently think 5.56 NATO as opposed to 7.62 NATO (NOT PISTOL CALIBER!!!), it could fire fully automatic but could be controlled in the hands of a trained soldier, and was "compact", think M16 versus the full sized battle rifle of the same time, the M14. Although a select fire equipped M14 basically fits the definition, too, regardless of caliber.
Such a rifle is not designed for long range shooting but, instead, primarily for nothing further than than a few hundred yards. Beyond that we're talking standard rifle calibers for long range, from .308 to .50 caliber and everything in between extant today.
I hope that clarifies the terminology somewhat. Just remember that because a rifle is not long, sleek, and stocked with fancy wood but with black polymer it doesn't become an assault rifle due to its appearance.