Full metal jacketed bullets aren't considered armor piercing, nor are those with a small "penetrator", such as .223/5.56. Soft point bullets also aren't considered armor piercing, nor are solid copper bullets that have a method to expand, such as skiving and hollowpoints.
A true armor piercing bullet consists of a copper or cupro-nickel jacket, a hardened steel core that takes up most of the inside of the jacket, and a small amount of lead to fill in the gaps between the jacket and core, and provide a cushion between the jacket and steel core. Most armor piercing bullets are made for rifles, but there have been rounds made for handguns, but those were mostly back in the 1930's and were referred to as "metal piercing" for shooting through car doors, etc. Those consisted of either a pointed steel cap over a lead core that also had a lead bearing surface, or of a solid zinc bullet that was of a round nose design. I've had both in my possession over the years.
U.S. Military armor piercing bullets will generally have a black tip. The nose of the bullet is dipped in black lacquer to show what the bullet is, but there are other colors used, too. Some will designate AP/Incendiary, tracer, etc.
There's more information about it, but these are the highlights.
Hope this helps.
Fred