Yes, of course! I love explaining stuff!
Piebald (or "pied") is the general term for white spots on an animal. There are piebald mice, rats, robins, snakes, horses, and even people. All animals with white spotting can be called "piebald." This Wikipedia page gives a brief overview:
http://en.wikipedia.org/wiki/Piebald When in doubt, it's safe to say a mouse with white spots is piebald.
Broken, Even, Variegated, Rumpwhite, Belted, Banded (and perhaps others I've forgotten!) are specific terms for white spotting laid out in the standards of mouse clubs. They are all used to say how a mouse is
supposed to look.
Genetically, Broken and Even are usually both s/s. This is the most variable kind of white spotting, as it can show up as just one unpigmented foot, or an entirely white mouse.
Variegated, as laid out for the show standards, is a mouse whose white hairs are more interspersed. I don't breed marked varieties, but it is my understanding that variegated comes in "show variegated" and "what most people call variegated but which is not, really" as well. The same might be true for banded, belted, and rumpwhite but I don't know that for sure.
The patterns of white spotting have different modes of inheritance. Some are dominant, some are recessive. One (either belted or banded, I can't remember) is dominant with incomplete penetrance, and variegated is a homozygous lethal dominant.
To get back to the original question, people seem to use "broken" to mean "erratically-placed white spotting which does not fall into any of the other spotting categories," but that's not what's meant for people who breed broken for show. I personally never liked the term. I think it makes mice sound like they are somehow damaged or in need of an arm cast.
