what is an armor piercing bullet?

[Amishman]

4. it depends on if you mean the legal definition or the practical definition

The legal definition is:

Under federal law, armor-piercing ammunition is defined as any projectile or projectile core that may be used in a handgun and that is constructed entirely from one or a combination of tungsten alloys, steel, iron, brass, bronze, beryllium copper, or depleted uranium.

So technically just about anything sold, even almost army surplus ammunition, is legally not armor piercing. But plenty of stuff that is not officially armor piercing will go through a vest.