Difference between vecino and residente?

I always assumed that "vecino" and "residente" meant the same thing, referring to the place an individual resided. However, I'm reading a baptism certificate that really got me confused it says that the parents of the child were: "vecinos de la Agua Dulce y residentes en este Pueblo [Atotonilco el Bajo]"

Where did these people live, la Agua Dulce or Atotonilco el Bajo? These two locations are close to each other, but I'm comfused because I always thought vecino and residente were sYnonyms.

Steve in NC