Interesting topic:
I've been told for most of my life that I'm quite smart (by teachers, parents' friends, psychiatrists… that last one was a joke. sort of).
In 4th grade my teacher said that what made me above average was the fact that I excelled in both in areas that require the right side of the brain, as well as the left (those being, math, science, and music as compared to writing, languages, and visual arts). As a result, while I've certainly encountered peers who could outrank me in one particular field, they are usually lopsided in favor of that field, whereas I'm more of a jack of all trades.
Academically I never got less than a A in grade school, and I was valedictorian of my middle school and high school graduating classes.
However, my entire perspective on my own "intelligence," as well as my self-esteem, were shot as of last year, when I started college at Dartmouth (an Ivy League school that nobody seems to have heard of). In grade school I was the top dog, the big fish in the little pond, unmatched, but now I'm surrounded by classmates who've effectively turned my little pond into an ocean (30% of them were valedictorians themselves). I've received Bs and I've developed an inferiority complex (academically).
That said, I'm still confident in my own "natural" intelligence, and still periodically have disdain for kids who spend hours studying in order to outrank me, but haven't an ounce of common sense or natural talent. So yeah, I don't consider being in AP classes or having a large vocabulary evidence of being smart. Intelligence is far more about cognitive thinking and the like.
Lesson here: if you're still in grade school and are apparently hot shit, get ready for a let down. The world is far bigger than the tiny one you've lived in so far, and there will always be people "smarter" than you.