The ability to generalise, or otherwise apply previous knowledge and experience to an otherwise novel problem. The ability to do so at speed is also a large factor, though slow but correct can also be acceptable, depending on the subtask.

Intelligence obviously breaks down into a myriad of sub forms. The obvious, and easily tested are things like spatial reasoning, or word games. Maths and logic puzzle solving also fall into the same group. These are used to form most IQ tests. Beyond that however are forms that are harder to measure, social intelligence is one such. Along with things like lie detection or reliable deception.

In most research, IQ is used. It has massive flaws, but is still useful. It tends to be an accurate proxy for full intelligence, at least at a statistical level. It's also useful for relative level comparison. E.g. a maths IQ of 100 would be average. In an average person, that would be normal. However, if their overall IQ was 160, then it's actually a significant deficit. It would point towards something like dyscalculia. Conversely, in someone with a significant deficit, it can point to an area of particular skill. Shaping their teaching method to lean on that area would likely help overall learning.

Basically, intelligence is a huge can of worms, once you dig into it. IQ akin to using GDP to measure countries. It has its uses, but you have to be careful with it, since it can hide a lot of flaws.

Another point to consider is that intelligence/being smart is a learned and practiced skill. The best potential bodybuilder in the world won't reach their potential drinking beer in front of the TV. A potential smart person can't actualise that potential without effort and practice.