An introvert can be described as a person that is the "opposite" of a extrovert. This person doesn't have to be quiet and unapprochable at all..it's just a person who feels at ease and prefers it when they can get some alone time. Theres nothing cool 또는 special with that, as many likes to imply for some reason.
An example; a extremely sociable person who frequently at times just doesn't bother talking with anyone at all to recharge can be a introvert. And vice versa, as there are quiet people who can be quite talkactive and HATES being alone and not socialising, they are still extroverts.
Social anxiety however, is what 당신 could consider a mental "illness", in the way that it makes it impossible for 당신 to function as 당신 normally should do. A socially anxious person may find it hell to be in ANY type of social situation, because they show sympthoms of anxiety when they go through it. (they may start shaking, sweat a lot, blush, feel uneasy, stutter and etc). As a result they completly start avoiding any social situation that triggers theirs symptoms (avoiding school, avoiding speeches and public situations, etc) It's definitely not associated with anything positive, unlike introvertedness.
TDLR; one is a personality trait, the other one a illness.