I would distinguish social anxiety from shyness like so:
A person who is shy will feel somewhat anxious about a difficult situation where people are involved, but they won't necessarily avoid it - this was me, aged 11. I volunteered to speak the first lines, alone on the stage, for a school play - I was perhaps a little scared, but I did it. Parents were filming it. The room was dark; the only light was on me. I read my lines, and when I was finished, it was over - I didn't have to think about what people were thinking of me, or the things that I did wrong. I was just shy, that's all.
With social anxiety, which for me began to develop in high school, the anxiety becomes overwhelming, and there's often a desire to avoid most or all difficult social situations. The shy-me performed in school plays; the anxiety-me began to avoid everything, and just a few months ago I struggled to share a two minute presentation with three students and my tutor. That's what I believe to be the key difference: with shyness, you can still do things, you don't dwell for hours on how you came across to an audience. With social anxiety, it's all switched up to 11 and hooked up to an amplifier.
Another important thing, though, is that there are varying degrees of social anxiety. Some people here are anxious about only one or two situations in particular - other people are anxious about them all, but perhaps less or more anxious than others. I'm terrified of walking through town or even through the park, especially if I'm alone, but I've never been any more afraid of authority figures than I am of anyone else, and I've read that that's a common trait of social anxiety. It varies from person to person, but based on my own experiences, it's fairly easy to distinguish between the two. Maybe there are shy people more shy than I was but without social anxiety - that's possible. I guess they wouldn't be able to compare it without knowing what extreme social anxiety feels like.