The LMG or L110A1 IS a LIGHT MACHINE GUN because Its a belt fed weapon that is light enough to be man portable.
Most light machine guns are not used nower days to engage armored vehicles anyway
The .50 or HMG is as it can smash optics on armored fighting vehichels 5.56mm can't.
The light machine guns main use is to engage enemy forces at ranges 600m and below and its designed to maim or wound the enemy instead of out-rite kill them.
SAW is an American term which categorizes any weapon that fires automatic only at a squad level.
The current animations for the LMG are fine in my opinon.
"The Medium Machine Gun" or as we call it General purpose machine gun is a crew served weapon, it takes two men to effectivly use the GPMG althou it can be operated by one man the sheer weight of it in the "Light" role means that to carry all the ammo you need two guys.
So the diffrence between the LMG and the GPMG Light role is that the LMG is a lot lighter and more mobile. And can be used in CQB with better effect then the longer heavyer GPMG, as the pictures show.
Were as the GPMG in the "light Role" just means that its not tripoded up and not being used for sustained fire to cover a company attack etc.
Its being used for mobility warfare so it can be set and displaced in a heart beat. Much like how the germans used to use the mg34 in WW2.