Difference betwee Rational and logical thinking

Rational means it makes logical sense in a mathematical, quantifiable way. Think Spock from Star Trek, or even Dr. Manhattan from The Watchmen. At times, they are coldly rational and only consider pure logic even if absurd moral or ethical sacrifice is involved.

Reasonable means it is a logical judgement, and makes sense in a fair and sensible way. Everything is considered from all conce
ed perspectives when saying something is reasonable. Absolute, quantifiable, rational information may be overridden to make a reasonable decision.

Example 1: The vast majority of scientists agree global warming is happening based off the data obtained, but it is not reasonable to expect people and industry to quit using fossil fuels cold turkey, even if the habitability of Earth is at stake. Some may disagree with that, but a sudden stoppage of fossil fuel consumption would cripple the economy and society at large.

Example 2: Evidence that is beyond reasonable doubt is the standard of evidence required to validate a criminal conviction in most adversarial legal systems. Doubt can be impossible to quantify. Logic does have to be considered in making judicial decisions but many times the situations need to be analyzed against how reasonable they are. Making reasonable judgements takes into account rational thought as well as other factors or motives. This is why this sentence is not phrase, "beyond rational doubt".