ad vs ap
The damage type. AD deals physical damage, blocked by armor; AP deals magic damage, blocked by magic resist. Every defensive choice in the game rests on that difference.
ad
AD, attack damage: physical damage, the kind dealt by basic attacks and by the spells of most marksmen, fighters and assassins. An AD champion buys attack damage and armor penetration; you defend against them with armor. "all ad" describes a whole team built on it.
open the page →ap
AP, ability power: spell power, the stat of mages and some supports. The damage is magic, reduced by magic resist. "build mr all ap" is the advice that goes with it.
open the page →Why they get mixed up
They get confused because they are used like role names ("an ap mid") when they are damage types. The trap is in the shop: buying armor against an AP team does nothing, and it is the most common defensive mistake in the game. Looking at the enemy comp in champ select settles it.