In BJJ, at least what I was told, a white belt is where you will be for some time. A blue belt means you have a good foundation and are starting to get to a point where you see the different strategies and where things go.....A purple belt means you have developed a really good defense, but offensively, you may struggle against higher ranks.....a brown belt has a really solid defense, is really developing an incredible offense, and then when you advance to black belt, you have just a really complete, solid game all the way around...Perhaps Tony or one of the other BJJ folks can weigh in.
In Aikikai Aikido, there aren't really colored belts. Some dojos have them, but at hombu, it's traditional white to black. As I said before, in Aikido, it will take at least 6 years, if not 10 or more. One of my fellow students just took his shodan exam....after 18 years of study. He was eligible 7 years ago, but really didn't care about testing.
There is also, if you are having this discussion, variation by where you are learning. In Japan, when you visit, they will say "OH, you're an American Black Belt".....They reach Black Belt faster in Aikido in Japan, and typically, a nikkyu or second kyu here in the US, would be equivalent to a shodan in Japan. There is MAJOR reason for this.....that is teaching.
In the US, it is very typical for a Shodan or 1st degree black belt to be teaching...that is unheard of in Japan. It's rare for anyone below the rank of Sandan (3rd degree) to teach, you may find a Nidan teaching a children's class, but most of the teachers are Yondan or above. So, there is a difference there as well.
Mike