From the foggy recesses of distant memories....
The original M193 was not the accepted NATO round. Instead, NATO standardized on the M109 62 grain bullet.
At close range, M193 penetrates steel better than a jacketed lead 62 grain bullet at the same speed. The M193 is faster, and speed is essential for drilling holes in steel.
The small steel penetrator in the M855 was added to create a 62 grain bullet that penetrates roughly as well as the M193.
The mission of the M855 is to penetrate a Russian soldier's helmet.
Not quite.
In establishing penetration performance, you establish what is known as V50. This is the velocity that 50% of the shots will achieve complete penetration. This is done by varying the charge weight (and thus velocity) and shooting at a fixed range at a target. Some shots will penetrate, some won’t. After you shoot a statistically valid sample of shots over a range of velocities, you can find the velocity where statistically half of the shot will penetrate. The lower the V50, the better the penetration performance of that bullet against that armor level.
From there, you use statistical methods to calculate the velocity that 100% of the shots will achieve complete penetration, V100. Once you have this velocity, you compare it to the exterior ballistics and estimate the range at which the bullet slows to V100.
M193 V50 against 3/8 steel is around 2840 fps
M855 V50 against 3/8 steel is around 2670 fps
The same is true for all metallic armor, M855 will always have a lower V50.
M193 V50 against 3 mm RHA is around 2290 fps
M885 V50 against 3 mm RHA is around 2000 fps
As to the development of 5.56mm NATO:
5.56mm NATO was created because it was well know that the 55 grain FMJ-BT was not achieving the maximum potential of the cartridge. There were two major schools of thought in the US:
1) A longer bullet would have better exterior ballistic properties, the XM287 was a 68 grain FMJ-BT developed back in the mid 1960's for the Stoner 63 to improve long range performance in the MG versions. The Vm was around 2950 fps. While it starts at a lower Vm, it retains more velocity down range, yielding a better maximum effective range. However, this would require a tighter rifling twist, at least 1-10.
2) Improved bullet structure would improve penetration performance, M2 Armor Piercing ammunition was always preferred combat ammunition over M2 Ball. By making an approximately 55 grain bullet with better internal structure better long range and short range performance could be achieved, but at a higher per bullet cost, but could use the same barrel as the current M16A1.
The second school won out and the US developed the XM777. Basically it was a scaled down version of the 7.62mm Armor Piercing, M61.
The Belgians combined the two schools of thought and came up with the SS109, which had the advantages of both, and well as the disadvantages of both.