I see people online throwing around IQ numbers constantly and everyone seems to think 120 makes them a genius. I want to know what the actual cutoffs mean statistically and what real world differences exist between someone at 110 versus 120 versus 130 and above. Is there a meaningful cognitive difference between those ranges or are people just attaching too much meaning to small score differences?
The cutoffs mean something statistically but the differences between adjacent scores are more gradient than categorical 
The population mean is 100 with a standard deviation of 15. A score of 115 puts you in roughly the top 16 percent, 120 is around top 9 percent, 125 is around top 5 percent, and 130 crosses into the top 2 percent which is the traditional threshold for giftedness. So yes 120 is genuinely above average and meaningfully so, but it is not the same league as 130 and above. The real world differences between these ranges show up most clearly in the complexity of work someone gravitates toward and excels at, how quickly they acquire new skills, and how well they handle novel problems with no prior framework. The gaps feel abstract until you see them play out over years of education and career outcomes.
120 is legitimately impressive and most people claiming it online probably do not actually have it 
130 is genuinely rare, roughly 1 in 50 people. If everyone in your social circle seems to be scoring 135 plus on their online quiz results, the test is flattering them, not measuring them 