Generally - yes.
The Bundeswehr MG3 and his short story:
MG1 - postwar produced MG42, called MG42/59, with changes at the breech for a slower rate of fire and in 7,62x51 NATO, later renamed to MG1
MG1 A1 / A2 - prototypes
MG1 A3 - new recoil intensifier
MG1 A4 / A5 - coaxially tank MGs
MG2 - wartime produced MG42, converted to NATO-caliber...
MG3 - some major improvements, like four new barrels with different profiles and coatings, option to use the M60-belt and many minor improvements.
MG3 A1 - coaxially tank MG
From 1968 on, all MG1/MG2 were converted to MG3 standard.
MG MRH 3 A3 - wartime produced MG42 (without AA-sight), converted to 7,62x62 NATO by Manurhin. Only used by the West-Berlin Police.