Intelligence is the raw processing power of brain. It is biological; it remains more or less constant during adult life. It is like a brain speed and short-term memory capacity. Computer analogy: processor frequency and RAM memory. IQ tests are trying to measure this brain power, not a specific skill. Different IQ tests may use different types of simple tasks, and yet their results highly correlate.

Rationality is how you use your brain. It can be learned (and LW is trying to teach it). Computer analogy: software with its features and bugs. Rationality allows you to reach nontrivial goals, where the raw brain power is not enough, it must be also used properly. Without rationality, you can expend a lot of mental energy and yet never reach your goals, as if you are running quickly but in a wrong direction.

EQ measures a specific area of skills.

In a very simplified metaphor, I would say that in a landscape of thoughts intelligent people "explore quickly" and rational people "navigate carefully". Low intelligence + low rationality = stays at the start or slowly follows the mob. High intelligence + low rationality = runs wildly everywhere, sometimes falls in a pit and cannot move from there (see Mensa). High intelligence + high rationality = avoids dangerous places and walks towards a distant goal.