First, welcome to the forum, David'sMommy. I hope you find lots of helpful stories and advice here. So much can be gleaned just by digging through the archives. And, of course, we love to help answers questions / provide insight / share experiences as well.
I think he's... bright. But, is he gifted? What exactly does that even mean? When I think of gifted I think of little geniuses who graduate high school when they are 10... I don't think of my little guy.
Well, some may, but that is by far not the majority of gifted kids. Gifted does not necessarily mean accelerated. Unfortunately, I think shows like Child Genius in some ways perpetrate the myth that, in order to be gifted, you have to be able to perform at that level. In reality, most gifted kids (and even some kids who would have fallen into the old "genius" category) might seem like normal, extremely well-adjusted and sociable kids (I have one of these).
He was really pretty average until some time between 2 and 3 years old. at one point when he was 2 I actually had wondered if he had a delay but at some point that changed. By the time he started pre-school he was wowing his teacher with the full sentences and big words he was using.
Sounds really familiar, as you basically described my DS. He's the kind of kid that has processes lots of stuff in his head before he can demonstrate something, but then, once he does demonstrate it, it's superior to his age mates. Often by a long shot. He did this with reading as well (went from being able to read basic, broken sentences on week to being able to read at the 4th grade level the next).
He has not been tested yet. The only test I am aware the school has performed on him is the STAR Early literacy test. He got a 812 on it and he's in the 98th percentile. I wish they tested for math....I don't know if testing him is the right thing to do and if it is even where to start.
One thing I'd recommend at this point is that, if you do take him to get an individual intelligence assessment (particularly if you are considering the Wechsler), wait until he is 6 so that he can take the WISC. It has a higher ceiling than the WPPSI.
Best of luck!
