Alto, or Mezzo?

Well, we can't really help you much without hearing your voice. These classifications have to do with tone and not, contrary to popular belief, with range.

Mezzos have a richer, darker tone than sopranos. And contraltos are even darker and richer than mezzos.

Also, I just want to ask why exactly you have two voice teachers? It seems like that might lead to a lot of dilemmas as to who is right...

If it's in a musical theater context, the term alto isn't often used. It is used more to describe a voice part in choral groups and classical singing. Mezzo is a common musical theater term for someone who sings in a lower register. Sometimes people can be mezzo-sopranos in a musical theater setting and altos in a choral setting, or sometimes the two are different; an alto often has a lower register than a mezzo. It truly depends on the person.

I don't know if that made any sense...