No. All 5.56mm ammunition is not NATO standard.
Cartridge, 5.56mm, Ball, M193 is not NATO standard.
Cartridge, 5.56mm, Ball, M855 is NATO standard.
Similarly M196 tracer is not, M856 Tracer is.
I'll let you google the differences between M855 and M193.
As to the pressure...
It is not so much the propellant charge, as the chamber. SAAMI chambers have shorter throats, this makes military ammunition exhibit higher pressures in SAAMI chambers.
Military ammunition, when tested in military test barrels, have similar pressures to commercial ammunition, tested in commercial test barrels.
In the AR-15 world, there are almost no barrel manufacturers that offer true SAAMI spec chambers, they are all Military or longer throated hybrids that allow for use safe use of military ammunition.