10 degrees of black belt exist in Karate. But each belt has a meaning. The meaning of the 10th degree is "perfection", not in those exact words. Because some people rightly believe that no one can be perfect, some Karate programs have eliminanted the 10th degree. An example of this is the ATA program, they only have 9 degrees of black belt.
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Time and skill levels. When one earns a blackbelt, they typically realize how little they really know. In many places going from 1st to 2nd degree takes a minimum of two years additional training. Two to three another three years. The higher degree, the more skilled the practitioner. In some styles it takes at least a third degree to open a dojo.
Shodan means that you know all of the basics well. The transition from 1st to 2nd is about developing and controlling power. The third is about reconciling power with your humanity and developing a sense of spirituality.
That could depend on the school.
A 2nd Kyu or 2nd Gup is higher than a 3rd kyu or gup.
However, degrees are usually associated with Black belt, and the higher the number the higher the rank.
I would expect in this case that the 2nd degree is higher than the 3rd degree.