Hi Diana,
I assume you are asking about the Australian designation, and to a certain extent, that depends on what document you happen to be reading. When first introduced in 1962, it was 'GPMG M60'; the 1967 EMEI defines it as 'Gun, Machine, 7.62mm, M60' and the 1975 EMEI calls it 'Machine Gun 7.62mm, M60'. These all refer to the 'standard' weapon, with butt, pistol-grip trigger group, and bipod.
There was no differentiation in nomenclature when fitted to the M122 tripod in the sustained fire role (not that the early weapons delivered to Australia were useful in that regard: too many breakages, leading to some severe testing to ascertain why, and to introduce improvements at design/manufacturer level).
As far as I'm aware, the early design improvements introduced into US production did not change the weapon nomenclature: it was still the M60 when in the 'standard' configuration. A few (very few) instances call the improved version the M60A1, but I don't think that's an official description.
Mike