Personally I believe there can be overlap of schizoid and avoidant traits. Or after being avoidant for a while you can start to become more schizoid as a defense mechanism. Both lead to avoidance of social situations so can outwardly be kind of similar, but an avoidant would have more anxiety while a schizoid would feel more emptiness. They used to be the same diagnosis, schizoid-avoidant personality, in DSM II.

Here's something I read about it recently. Not sure this guy is the final authority on the matter but he seems legit: Avoidants

I still have social anxiety but I think I lean more schizoid now. I don't seem to want to be involved in relationships anymore (whereas I used to try to fit in and maintain friendships) and I have gotten more emotionally distant over time (at least outwardly).