The guys at Forgotten Weapons have done a great video which explains Machine Gun Terminology. Not only are there way too many different categories of machine guns, some of these terms have changed over time. Forgotten Weapons tells us who makes them, why they exist and their place in military history.

Automatic Rifle: Shoulder or hip fired, limited magazine capacity, minimal sustained fire capacity. Examples: M1918 BAR, Chauchat.
LMG: Magazine fed, rifle caliber, bipod fired. Examples: Bren, Madsen, Lewis.
HMG: Belt fed, usually water cooled, minimal portability, fired from tripod only. Examples: Maxim, Vickers, Hotchkiss 1914. Evolved into guns of caliber 12.7mm – 20mm, like the M2 and DShK.
MMG: Air cooled, tripod fired only, belt fed. Examples: Browning 1919A4, SG-43.
GPMG: Bipod or tripod fired, belt fed, rifle caliber, quick-change barrel. Examples: MG42, PKM, M240.
SAW/LSW: Intermediate caliber, magazine fed, bipod fired. Examples: L86A1, FN Minimi, RPK.
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Photo courtesy of US Army. A New Jersey Army National Guard Soldier from fires his M249 SAW during live-fire battle drills on Joint Base McGuire-Dix-Lakehurst, N.J., April 9, 2018. (U.S. Air National Guard photo by Master Sgt. Matt Hecht)