The M16 uses a 5.56(0.224) bullet.
The AK47 M43 uses a 7.62(0.311) bullet
The M60/M1A uses 7.62(0.308) bullet.
None of those three will interchange. The 5.56x45 NATO is smaller in bullet diameter, and case diameter than 7.62x39 Russian. It is also longer(45mm vs 39mm, or about 1/4".
The 7.62x39 Russian will not interchange with a 7.62x51 NATO. The Russian round is not the same diameter, even though both are "7.62". The Russian round mic's out at 0.311", as compared to 0.308" for the NATO/Winchester round. The NATO round is also 11mm longer.
I have all three sitting on my reloading bench at home. They are three totally, completely different animals.
There is an AK-101 made for export that used the 5.56NATO round exclusively. But, that is pretty recent(1994).
I would be very interested to find out more details about the cartridges that you swapped in different weapons, and the weapons themselves, though.