When I was in school, the "brightest" were pulled aside (with parental permission) and given IQ tests. On the scale used (not sure if it's same now or worldwide) if you scored 130 or higher, you were considered gifted. I had already had to test in to start kindergarten early (at age 4, since I have a late birthday) and passed with flying colors. I was tested for gifted in 2nd grade (the earliest you could start the program was 3rd, so a lot of testing was done in 2nd so they could start gifted at the beginning of 3rd).
Now, so far as I know, Kiddo has NOT had an official IQ test, or if they did I know nothing about it. But her standardized test scores, grammar, and vocabulary have consistently been well above most of her peers and even with her behavioral issues her teachers always (so far) have recognized her as "one of the brightest kids I've ever had in class." And these are not new teachers by any means - her 2nd grade teacher taught her 1st grade teacher (and 2nd grade teacher won the Golden Apple Award the other year as an outstanding teacher in a multi-county area). This is a kid that can trip dinosaur names off her tongue like a professional (and I'm sure there's plenty of boys who can do that at her age, but most girls aren't interested) but also comes to me with the scientific names of other animals and asks if they're derived from Latin or Greek, which I doubt is a very common question for any kids her age. Heck, most adults I know don't ask some of her questions!
She's one of those kids, that on a good day with a subject that interests her, is "an absolute joy to teach." You can almost see the gears whirring in her head as she asks questions that are totally unexpected and you can hear the answers click into place and launch new questions. She picked up things fast when she was little, could spell her name before she was 2, was speaking in full sentences before that, knew her shapes (above and beyond, like octagons, diamonds, hexagons, etc) by 18 months, knew colors by look and word (not just basic ones), and 1-10 by numbers and words by then, too. Her pediatrician's nurse used to take her in the back and show her off to the other nurses!
Yes, there are different types of gifted, more recognized today than back when I was in school (and I'm likely a little older than you, but it sounds like in the schools I went to you would have been tested as well). We were determined as "academically gifted" and had a special program for it. I wish they had a gifted program like it here. It was in that program that I met more "quirky" kids like me from other schools as well as my own, and it makes you not feel so alone in your "strangeness" even if their quirks are different from your own. But you know what? As intelligent as most of us were ("booksmarts") most of us were (and some still are, like me) fairly "people stupid." We don't socialize well, we don't "get it." In retrospect, I wonder how many of us are Aspies or close to it.