There is reflexive intelligence which is useful on the time scale of sports, IQ which is useful on the time scale of a math test, and wisdom which is useful on the time scale of a lifetime or several generations

I agree with your assessment of the first type of intelligence. Reflexive (physical, athletic) intelligence is useful to the individual (or small band) on an immediate time scale. It was probably much more important in the distant past than in modern society. Its impact does not go far beyond the individual who wields it. I think of this type of intelligence as a low-level (in a non-pejorative sense), animal type of intelligence. It is always manipulated and harnessed by wielders of higher-level types of intelligence. What of lasting significance can a pro athlete, or even an outstanding soldier, achieve, compared to the sports tycoon (or corporation composed of high-IQ individuals) who buys and sells athletes, or a staff-level general, responsible for decisions that affect the fate of nations? This is a question of both time scales and scales of groups and group-affecting actions.

I think IQ is a combination of both innate and trained logical, pattern-recognition, technical problem-solving type intelligence. Its useful time scale might range from the immediate to the middle-term. I think in the longer term things become more complex and unpredictable, and less manageable by this type of intelligence alone. (On historical time scales, one needs to deploy all types of intelligence optimally to have a lasting impact.)

Wisdom is a more elusive term, but I think OP has it right that wisdom is "knowing where to aim". Wisdom could be anything from immediate-term common sense (street smarts) to middle-term social cunning or business acumen to long-term awareness of and alignment with basic time-tested life principles (on both individual and societal scales).