rational v/s logical

Yesterday, while out at Crane beach with a bunch of friends and friends of friends, I was randomly asked the question - "you seem like someone who would know the answer to this: what is the difference between rational and logical".

I'm not sure what caused me greater pause for thought - why someone I just met had already pegged me as a person who could answer that question, or the question itself. And yes, why bring this up at the beach, where I would rather be sleeping in the sun or reading vapid chick-lit.

Well, rational as opposed to irrational is the first thing that came to mind. I thought of rational v/s irrational numbers - one is tangible and the other is not. Or are those real v/s unreal numbers - I forget.

I looked up Oxford for the definitions of both:

rational:
1) based on or in accordance with reason or logic
2) having the capacity to reason.
3) able to think sensibly or logically.

logical:
1) of or according to the rules of logic.
2) capable of or showing rational thought.
3) expected or reasonable under the circumstances.

So if there's logic in rationalism, and rationalism in logic, what indeed is the difference?

Possibly the difference between the ability to see reason, and the ability to reason things out?
Logical is generally based on a sequence of thoughts or events.

What other words exist where the difference in the definitions are so subtle, and yet the meanings themseleves are quite different?