Guage is kind of a weird system, the smaller the number, the larger the balls and, usually, the more powerful the cartridge.
This article gets rather technical, but it's very good:
Gauge (bore diameter) - Wikipedia, the free encyclopedia
So, .410 (caliber, which is equal to 67.5ga) will be less powerful than a 20 guage which is less powerful than 12ga which is less powerful than 10ga, etc.
As for distance, it's going to depend on what kind of shot/slug is used and how "hot" or powerful the shotshell is.