The original profile was thin. It is generally referred to as an A1 profile when the barrel is the original 20" barrel length, but is also referred to as 'pencil'. Bushmaster calls their 16" pencil barrel a lightweight. I don't have the exact numbers in front of me but it is very small. It even uses a different sized front sight base.
The military later switched to heaver A2 profile. This is what is generally meant by a government profile, especially on 20" barrels
The M4 profile is basically the same as the government profile except that it is used on carbine barrels and has the extra cut out front for the grenade launcher.
Some companies started producing the HBAR barrels, which look like a government profile until you remove the handguards and see that the manufacturer saved money by not reducing the profile under the handguards.
A2, M4, Govt, HBAR and pretty much everything else use the same size front sight base/gas block.
Then there are bull barrels that are heavy along the whole length of the barrel. These also use a much larger gas block/front sight base.
Edited to add the SPR profile, which is heavier than the govt profiles but lighter than an HBAR.