I think the difference might have to do with context. Most of my adult life has been spent surrounded by people who are gifted. Once you're dealing only with people in the tail, the identity of "gifted" is no longer that important. It doesn't really say very much about who you are or distinguish you from everyone else well. So, if it's something you talk about, then it's like you're missing the point.
... If I switch to the public school reference frame, gifted becomes meaningful again.
I agree that giftedness is always in respect to 'what people are supposed to be like' and if a teen self-identifies as gifted, then they are more likely to set up their marriages, their worklife, etc were they get a good healthy serving of peers. I don't think that anyone needs to spend 'all' their time with people who are like themselves in any dimension, but I am happy Kcab, that what we call gifted out here is the norm where you are.
Because no one thought of me as gifted while I was choosing my career, there was no one to suggest to me that I might want to include daily contact with peers as a value. This isn't exactly true - I was recognized as 'bright' and choose a career with lots of bright people in it, although not much opportunity to connect with those bright people after the training phase was over. At the post college level, I still had classmates sighing with unhappiness whenever a teacher called on me with my constantly raised hand - so I think there was a LOG mismatch. This was confirmed as time went by, and yet I was totally believing that 'different = worse than' story.
((shrug))
We live and learn,
Grinity