Is there a difference between amateur and professional dan levels in go? If yes, how are they related?
For amateurs, each level is one stone difference. So an amateur seven dan is six stones stronger than an amateur shodan. "Seven dan" is about as strong as a "pure" amateur is likely to get, although there are some amateurs that have had professionalized training, and are believe to be "eight dan" in strength, on the amateur scale.
"Pro" starts about where amateurs leave off. That is a pro one dan is about an amateur seven dan. Pro dan levels go from one to nine, but the difference in each level is about one third of a stone, rather than a whole stone. So a pro nine dan might be a "ten" dan on the amateur scale.