Registering is optional as in you do not have to.
Activation is what is needed to use XP (trial for 30 days).
"I have a PC at home and also at my weekend retreat and since I use a removable disc which is transported between homes would this present a problem to XP re the registration business." - Yes as XP would see the weekend retreat as a new computer (which it is). XP can only be one the one computer. You cannot have it on both i'm afraid even though you have a removable drive.
Info: click here
You'll have to buy another copy of XP.
XP home and Pro...
The same apart from "pro" has extra Networking, file encryption...