I think most introverts know that they are. Most extroverts I’ve met, on the other hand, don’t seem to be aware of the two definitions at all. They assume everyone is like them… which is not entirely unfounded. 70% of people are extroverts — using the proper definition of the term.
For those who’ve never heard the proper definition, here’s a great article highlighting some of the differences in personality types. Its a useful read, and as an introvert, I wish more extroverts took the time to understand the subject matter. Here’s one of my favorite lines:
Perhaps the hardest thing for extraverts to understand about introverts is that someone could actually want to be alone. Not because they don’t like to have fun, or because they hate people, but just because they prefer their internal world, and they need to return to it to be energized.