As a general rule, a score of 130 on an IQ test places a child 2 standard deviations from the “norm”, or roughly in the 98th percentile. About 1 child in 50 will score this highly. This is usually the cutoff for calling a child “gifted”, and kids in this range are usually referred to by the gifted psychology/education community as “moderated gifted”. These are bright kids who are usually fairly normal socially. These kids are often in G&T programs, AP courses, and programs like Johns Hopkins CTY or Duke TIP. Elite colleges are full of them (and full of a lot of kids who score just below this; Duke TIP uses a score of 125 as a cutoff for it’s programs, which is about the 95th percentile). Many of these kids have great leadership qualities, as they are bright and talented, but not so far from the norm that they are isolated. Many are socially extroverted.
A score of 145 on an IQ test places a child 3 standard deviations from the norm, or roughly in the 99.9th percentile. Ab out 1 child in 1000 will score this highly. This is the cutoff that Davidson uses - they call it “profoundly gifted”, though the general parlance in the gifted psychology community is “highly gifted”. This is also the rough minimum that you usually find kids who qualified for Johns Hopkins SET. Kids in this range tend to accelerate more, but may or may not stand out.
A score of 160 on an IQ test places a test 4 standard deviations from the norm, or roughly in the 99.999th percentile. These kids absolutely need acceleration, and will be terribly bored if grouped with other kids. They tend to be more introverted, and to have more social difficulties because they have more synchronicity compared to the general population. Above this level usually increases these aspects.
These are gross generalizations, and I’m by no means advocating IQ testing as the sole arbiter of giftedness. But in general, the 4SD+ child is as far removed from the “normally talented”/“moderately gifted” as those children are from the norm.
Julian Stanley (formerly at Johns Hopkins) developed the concept of above-level testing to identify the highly, exceptionally and profoundly gifted. Two 12 year olds may score in the 98th percentile on a standardized grade level test; but give them both the SAT and one may score a 350 and the other a 750. The first kid is “normally talented” and will generally do well progressing through the standard curriculum at grade level through G&T, honors courses, APs, etc. The second child needs acceleration. It’s not perfect, but it remains a decent screening tool.
The child in the OP is in the 1 in a million range by multiple measures - the age at which he learned to read and learn math and languages, his scores on above level tests, his degree of acceleration. Nothing will change that. Socialization is good, but he’s going to be an extreme outlier, and expecting him to develop socially according to the norms of less gifted kids is probably an exercise in futility.