Networks : Workgroups and Domains. How Do I Use Them?

I have three PCs. Call them D, A and M. M was a W2K machine until I just
installed XP Pro. D is my desktop in the den, and most used. All three
could reach one another via my LAN prior to M becoming XP, but now M is
not getting the idea it's on the LAN. I'm sure I've configured its
ethernet adapter properly. I think the problem is from my lack of
understanding whether these machines are together as a workgroup or
domain. I may have just been lucky with the previous LAN that had M (W2K
then). The only good source I have for making a LAN has been my QUE
Using MS Windows 2000 Pro book. It's been getting me closer to a solution.

Right now I have all three PCs set with a workgroup called AXY. Somehow
I have a mixture of three different domain names. I'm running as a
business network. If I want to configure solely for a workgroup network,
then I would think I do not need to provide a domain name, and vice
versa for a domain network. How would the network know which type of
network I'm using, domain or workgroup?

Perhaps someone could provide an example of how the computer, domain,
and workgroup names should be used for my situation, that is, wanting to
use a workgroup network?