I think that for many kids the idea that profoundly gifted kids behave markedly differently from other children in all social settings is a stereotype. When the activity being done is something like swimming/soccer/playing tag, etc. many gifted kids look just like everybody else.
For our son, however, ages 3 and 4 were the worst. Kindergarten would have been pretty terrible if the school hadn't realized that they needed to make accommodations for him.
We also had him in a daycare full of the children of professors/law students/medical students, and our daycare provider told us when he was 8 months old that he was the smartest kid she'd ever worked with. We wrote her off as having rose-colored glasses about him because she adored him so much, and we didn't think a baby could do much to set himself apart from the other babies. We pulled him at her suggestion and sent him to a preschool (not her suggestion of school) and it was disastrous.
Now, the test results we have show that he is in fact probably the smartest kid she'd ever worked with, but he still behaves like a regular kid most of the time.
