The SAT and the GRE are IQ tests. They have the same psychometric characteristics and reveal the same information about testees. They correlate with IQ tests at the same level that different IQ tests correlate with each other. Results from IQ tests explain very large amounts of the variance in SAT and GRE scores, and vice versa.
This is not a strictly necessary state of affairs - if large numbers of people who knew nothing about chemistry started taking the chemistry GRE, the strongest signal provided by the chemistry GRE would switch from "IQ" to "whether or not the person has ever studied chemistry".
But (1) the test would remain an IQ test once you ignored the very low scores of people who had no reason to take the test; and (2) in reality, people who have never studied chemistry don't take the chemistry GRE.
This is not a strictly necessary state of affairs - if large numbers of people who knew nothing about chemistry started taking the chemistry GRE, the strongest signal provided by the chemistry GRE would switch from "IQ" to "whether or not the person has ever studied chemistry".
But (1) the test would remain an IQ test once you ignored the very low scores of people who had no reason to take the test; and (2) in reality, people who have never studied chemistry don't take the chemistry GRE.