As far as I've encountered, both exists.
Observation tells me;
High IQ NTs are just NTs who are good with academics and are tend to be achievers.
But are otherwise emotionally and socially more age appropriate, can relate to other NTs. Their giftedness doesn't isolate them, but more like a talent they can just turn on and off.
Gifted due to being an ND, on the other hand... They're emotionally different as they are intellectually different. They do not relate well with NTs.
They either tend mask or go in isolation. Their giftedness is both a blessing and a curse -- it has no 'off switch' so to speak, likely to have what is called twice exceptional.
I wonder how correct this is. 
Also from what I've gathered, the latter is a more realistic portrayal of genius than the former.
The former could just be nerds or geeks but otherwise NTs who are just good at what they could do.