Is the affection that your Pokemon gets from Pokemon-amie the same as friendship? Or do they have any relation? Like if a Pokemon has full affection in poke-amie, will their friendship be raised?
No, Pokemon-Amie and friendship are completely different, and don't have a known relation.
However, the only Pokemon that can evolve with Pokemon-Amie is Eevee --> Sylveon, with Max Affection.
Hope I helped. :)