This is a great question, and one that I think all of us have asked at one point or another. It's good to get outside views, because when you have an out-of-the norm child, you just don't know what "average" looks like.
For me, I never considered my child as gifted before school. I knew she had the potential, her dad and her grandfather are both highly to profoundly gifted. I do know that from the beginning she was very different than other kids. We only had her tested because she was disruptive in the classroom. Turns out, she s gifted and has ADHD to boot. I base my identification of her as gifted based on her IQ on a WISC IV (i.e., IQ </= to 130) and on her academic level (for example, reading at a college level, including both comprehension and vocabulary in 4th grade).
For us, it's not a label. It's a tool to help us identify the right resources to help teach her and just to understand her. It goes back to "what gets measured, gets managed" for me. If she was doing fine in school, learning at her level, etc.. I wouldn't need the know the numbers. BUT it is helpful to have accurate numbers so you know how to find that right level of instruction that isn't too easy and yet not too hard. Having that formal identification is what also guided us to decide to homeschool again this upcoming year rather than continuing to force traditional schooling.
I hope this answers your questions. And YES you are doing right by your kids in advocating for them to be taught at their level. If the kids are getting what they need, that's awesome and you are very, very lucky.
And this is a safe place to talk about what our kids are doing, and that in and of itself is a blessing, because in general, talking about kids excelling in academics is seen negatively, unlike talking about your kid's talent in music, dance, the arts, or sports. Those things you can talk about. But celebrating that your child was accepted into a program like Center for Talented Youth at John Hopkins meets with a whole lot of silence (at least in my experience). I love hearing about other kids, many of whom are doing things I am amazed at and make those aspects of my daugher seem very average. And that's a good thing
. (edited to add: because she IS very "average" in many things, and that's okay too!!).
Welcome, and your kids sound awesome!