Light machineguns are MGs with Riflerounds of "standart" caliber, like 5.56x45mm, 7,62x51mm, 5.45x39mm, 7.62x39/54 etc. They are portable by ONE man and are deployed with a bipod.
Medium machineguns are the same MGs as above, only on a Tripod, which might be carried by 2 men or more, and is more or less sationary. Best example, MG3 and M240, which can be deployed either with a Bipod as an LMG, or with a Tripod as MMG, but both weight a hefty 25pounds (circa) with ammo and without bipod, so they arent Light in a weight matter.
Heavy MGs are usually bejond the Assaultriflerounds, usually 12.7mm (.50cal) MGs in either 12.7x99mm NATO or 12.7x109mm Russian, which NORMALLY can´t be moved around, like the M2 on Tripod...
But the Russian KORD MG and the newest lightweight .50cal MG from the US are both light enough to be carried around and deployed by one man. Still heavy things and around 30pounds without ammo or so but still alot lighter then the M2...
The KORD has even been fired on the move, so "heavy" just depends on your body-strengh XD
There´s a vid of it on YT btw.
It,s just military jargon...a LMG can be a MMG too, a HMG can weight much less then some MMGs, its just a matter of deployment (bipod, tripod) or caliber (HMG)
And SMGs...well, that´s english for you...
And no, usually LMGs fire much faster then HMGs, because an HMG with a huge rate of fire would create so much recoil that even the tripod wouldn´t be enough to control it, so they are pretty slow.