In the SciFi book "Children of Memory", Tchaikovsky at least splits intelligence into reasoning and recall. People also talk about system size and working set.
Persistence is another thing I've come to view differently. The mind is willing to entertain a problem as long as progress feels possible. I wonder if that feeling of possible progress is trainable. Another view of 'possible progress' is rational faith (lower case f, sorry I don't have a less loaded term, after all, many consider faith to be irrational).
But mainly, I think we are still in the dark ages of psychology, brain function, and theory of the mind. Thus it is important to me to be humble about how I talk about what intelligence might mean.
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By the way, I love the Children of Time series, but I had to really defocus my mind and suspend my disbelief and scientific critique to try to imagine other intelligences.