So the only skill this archer used, then, was archery? No melee at all, no light armor, nothing? Because I wanna know how you spent all your perk points then. Being an archer is one thing, using only the archery skill and no other skills is absurd. That isn't being an archer, that's being a monomaniac.
Ditto with the two-handed warrior: You only used the two-handed skill, no heavy or light armor, no sneak, no smithing to improve weapons, nothing at all?
Archery has to do with using...hmm let me guess bows?
Light armor has to do with what the character wears, it does not define weither he is still an archer or not.
The difference is...
If you called yourself a thunder mage and used fire, ice, and illusion spells, then you are not a thunder mage.