Armor and armour are the same word with the same meaning; only the country changes the spelling. Armor is standard American English, armour is standard British English. Think of it the same way as color and colour: drop the u for American readers, keep it for British ones.
The core difference
Armor and armour both mean a protective covering, spelled the American way and the British way.
- armor — the American spelling, for protective covering on people, vehicles, or objects: Modern tanks rely on layered armor to survive direct hits.
- armour — the British spelling, used the same way: The medieval suit of armour on display weighed over twenty kilograms.
How to tell them apart
There is no difference in meaning between armor and armour; both trace back through Old French armeure to the Latin armatura, meaning equipment. The word can also work as a verb, as in engineers armoring a truck's underside, and the same American-versus-British spelling split applies there too.
The mix-up shows up most often in gaming, film, and fantasy writing, where American titles use armor and British ones use armour. Sticking to one spelling consistently within a single piece of writing is the safest approach.
