An individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks.
IIRC general intelligence also doesn't simply measure speed of cognition, but also ability to choose what to focus on ("intuition"), which these tests do not measure.
Speed of cognition is absolutely correlated with IQ but the difference in speed doesn’t cause the differences in results. Both are downstream of being more intelligent.
> Speed of information processing and general intelligence
> One hundred university students were given five tests of speed-of-processing, measuring their speed of encoding, short-term memory scanning, long-term memory retrieval, efficiency of short-term memory storage and processing, and simple and choice reaction time or decision-making speed. They were also given the Wechsler Adult Intelligence Scale and the Raven Advanced Progression Matrices. A number of multiple regression analyses show that the cognitive processing measures are significantly related to IQ scores. Other analyses indicate that this relationship cannot be attributed to the common content shared by the reaction time and the intelligence tests, nor to the fact that parts of the WAIS are timed. It is concluded that the reaction time tests measure basic cognitive operations which are involved in many forms of intellectual behavior, and that individual differences in intelligence can be attributed, to a moderate extent, to variance in the speed or efficiency with which individuals can execute these operations
https://www.sciencedirect.com/science/article/abs/pii/016028...
> General and specific cognitive abilities were studied in intact Swedish same-sex twin pairs 80 or more years old for whom neither twin had major cognitive, sensory, or motor impairment. Resemblance for 110 identical twin pairs significantly exceeded resemblance for 130 fraternal same-sex twin pairs for all abilities. Maximum-likelihood model-fitting estimates of heritability were 62 percent for general cognitive ability, 55 percent for verbal ability, 32 percent for spatial ability, 62 percent for speed of processing, and 52 percent for …
https://www.researchgate.net/profile/Robert_Plomin/publicati...
This is great for Swedish people. The problem is that humanity consists largely of not-Swedish people. Same for most studies of this kind, which are largely concerned with populations that are already genetically closely related; it stands to reason that the differences between people who are closely related will be more attributable to their inborn differences, than the differences between people who are not closely related. They haven't been able to do an interracial, intercultural comparison on this because socioeconomic circumstances are so substantially different between groups (and have been so since the rise of modern empirical research) that it's impossible to set up a decent comparative study.
The g factor is highly heritable, and countless academic works and studies establish it as such, well beyond any reasonable doubt.
I tend to err on the side of caution with this one.