For me I'd say shyness is a style of communicating with others. Shy people may be quiet but still able to talk to others, just coming across as slightly awkward and more reserved than most.

SA is when it becomes a lot deeper so we may cease being able to communicate effectively in certain situations or spend a long time worrying about what others are thinking in a way a shy person may not. And I'd even suggest that some people with SA aren't shy at all - they may have confident underlying personalities that are completely hidden by the fear of being judged negatively by others or a fear of imagined social disasters.