I have a friend who's a metalworker. He'd never beat me in an algebra test, but he's damn smart when it comes to manipulating the physical world. He also happens to be very thoughtful and insightful about film and photography. But I'm not sure he considers himself "smart", even though he does original and careful analysis in the areas that he cares about.
Another friend is -- as far as I'm concerned -- an absolute genius at understanding people psychologically, their decisions and motivations. I'll never be as smart in my own preferred areas as she is in this. But I don't think that most people would give her a "smart" badge for it.
Often this comes up in written fiction: authors will describe the characters and their thoughts and motivations in a mode natural to how they perceive things: some authors spin up plots and intrigues at every turn, others focus on raw emoting.
So I tend to view smarts as a personality trait, when we're dealing with healthy folks with no other issues(and realistically, most people are battling something else most of the time without necessarily being aware of it). There's a limited degree of smarter-is-smarter that shows up in testing, and then after that it starts being about personality-driven specializations, the ways in which they overcome problems. The archetypes are easy to spot in school: the student who seems to ignore any lecture or materials and rushes to get help from the teacher or study buddies, versus the student who quietly reads the text and never asks a single question. Both types can get perfect scores in some subjects, but usually not across the board, effortlessly. And as projects grow in scope and cover more skills, awareness of personality-driven limitations becomes more essential to success.