armor vs mr
The damage type you block. Armor reduces physical damage, magic resist reduces magic damage. Neither protects you from the other.
armor
Armor is the defensive stat against physical damage: basic attacks, the spells of marksmen and fighters. You buy it against an AD team, and it gets countered with armor penetration. "build armor all ad".
open the page →mr
MR, magic resist: the defensive stat against magic damage, the kind mages deal. Same logic, other colour: "build mr all ap". Both stats sit on tank items, but rarely at the same price.
open the page →Why they get mixed up
It is the AD versus AP confusion, seen from the defensive side. The reflex that misleads: buying "tank" in general, without looking at where the damage comes from. A tank stacked with armor dies in three spells to a mage. The right question is not "am I tanky?" but "tanky against what?".