Here is Millon's quick overview of those 2 personalities:
http://www.millon.net/taxonomy/schizoid.htmhttp://www.millon.net/taxonomy/avoidant.htmEmotionally, avoidants and schizoids are total opposites. Avoidants are hypersensitive, while schizoids are hyposensitive. Avoidants tend to connect emotionally too much, so they try to stay away from people to avoid emotional pain. Schizoids are unable to connect emotionally, so they do not avoid people per see, they simply do not seek people since nobody seeks what they do not enjoy.
Since avoidants can connect, their isolation will be subjectively painful. They have a need for others that they cannot fill, so they will tend to feel lonely, feel inept and inferior because of their self-imposed isolation and tendency to escape from emotional pain instead of facing it.
Schizoids cannot connect, so their isolation will not be immediately painful. In the case of schizoids, the "angst" comes from somewhere else. Their incapacity to connect is not limited to people, but is rather part of a greater incapacity to connect emotionally at all, to anything. So they will be stuck with a general sense of emptiness, depersonalization, an incapacity to take pleasure in anything, a sense of boredom that they cannot get rid of no matter what they do (except drugs, but that is cheating the brain reward system).
So both tend to be loners and both tend to be prone to depression, but not for the same reasons, and it will not be the same "flavor" of depression. Avoidants tend to get the emotional/hot kind and schizoids tend to get the void/cold kind.