Hm. I think it’s inescapable that shyness and introversion are going to be close cousins. I think it also depends on which definition of shy one is subscribing to.
Shy can mean timid, wary, or bashful, which my dictionary describes as inclined to shrink from public attention. It can also mean to show a dislike.
And with the exception of timid, I think most of those words can describe many introverts’ reaction to being around large group of people or being in the spotlight. Because, yeah, we’re wary of stepping into a situation which is not our natural element. We have to be more on our toes, aware, we’re operating outside our comfort zone, and when doing that, it’s smart to be wary! Being shy or wary or cautious when not in our natural element is a really healthy, good thing.
And if bashful means to shrink from public attention, well, most of us do that too. It’s in the specifics of why we do it that our introverted individuality will come into play. And while the internal reasons may vary--whether it’s to conserve energy, or because being around that many people is an assault to our psyche, or we’re just uncomfortable--the behavior, shrinking from public attention, is fairly demonstrable.
I think this is further exacerbated by the fact that introverts are in the minority, and many extroverts won’t have the internal reference for understanding the reasons behind our actions; all they will see is the manifestation of the shy behavior. And thus we’re labeled shy. But it’s only one, very surface component of what being an introvert entails.