One distinction I always liked might be called "fertile" vs. "focused" intelligence.

Fertile intelligence is the ability to come up with ideas. People with fertile minds come up with lots of startling, original ideas ... and often lots of wrong ones. They're quick to recognize analogies ("Wow, X works just like Y!"). On the other hand they can get hung up on non sequiturs and ideas that seem neat but don't make sense. Maybe the real underlying skill here is very perceptive and quick pattern-matching.

Focused intelligence is the idea to see what's important and ignore the rest. People with focused minds aren't great at coming up with original ideas; they solve problems by saying "What's this problem really about?" and attacking it head-on. They're good at constructing logical arguments because they don't get sidetracked. They tend to be very predictable. They ignore things that "just might work" and stay where most of the probability mass is.

When a "fertile" mind solves a problem, you look at the solution and think "Wow, how did she ever think to do it that way?" When a "focused" mind solves a problem, you look at the solution and think "Wow, that's the only natural way to do it... why didn't everybody do it this way before?"

John Stuart Mill claimed that women tended to have fertile minds while men had focused minds (the words are my own, but I think I'm capturing his descriptions.) I'm not sure if it's true generally of men and women, but I do see people fall into those types.