Everyone avoids, everyone withdraws when sad or depressed...
We don't have a patent on that so, yes, they both read simular but the differences is in the response and reaction.

A person with SA is basically in charge of their own thoughts and triggered into varying degrees of dire straights by certain events, circumstances etc.

AvPD is personality, we don't have thoughts that haven't been induced by AvPD. (every thought!)
The Avoidance has shaped us into how we think, act and behave.
Since early childhood we have been mentally groomed, following and learning not from our parents or caregivers, but AvPD because that is/was the only thing that is constant and dependant in our lives. (there is a bit more to that as well)

That shaping of maladjusted thinking becomes our psyche with reinforcement to keep a tight grip on us.
Think about it if something so terrible was easy to escape from then we wouldn't be influenced as we are.

AvPD is recognisable on here and that's why we are quick to pick up those who don't have the disorder. That early childhood and onward AvPD nurturing is obvious as its like a accent or signature in, like I said their response, and reactions.

SA and AvPD can be worded simular as they are both Anxiety issues, but one has ongoing impact even during times of quiet where the other needs a match to ignite.

Your psych will work with you and cater your needs accordingly.
I'm really sorry about the wall of text.