It depends on the context, but I would generally use "faithful" when talking about two people in a relationship who do not cheat on each other (ie they do not have intimate relationships with anyone else).
I would use "loyal" in many ways. People can be loyal to the company they work for, to specific brands of clothing, to their friends etc. A dog is seen to be loyal to its owner if it follows them everywhere and does what it's told!
In many countries people plead loyalty to their king/president etc by taking things like an oath of allegiance.