What is the difference between brown and red belts?

Answer 1

In Taekwondo, the difference between a brown belt and a red belt is about six months of study; although this will vary from school to school.

In karate, the difference between a brown belt and a red belt is much more significant.

Answer 2

It depends on the style of martial art. In some styles a red belt is a rank between white belt and black belt, a couple years worth of training. In the traditional Okinawan styles, red belt is the highest level achievable, indicating a 9th or 10th degree black belt, which is a lifetime of training (40+ years).