You are correct. Any of the operating systems from Microsoft are (1) O/S one PC. The "Office" suites can be installed to (2) PC,s. (1) Desktop and (1) Laptop if they both belong to you and are being used by you.
You can install your XP O/S to your PC, then if you decide to use it with another one, you will need to remove from the first one, then install to second PC. You are allowed to do this, and will have no problem with "Activation". If it does not activate automatically over the net, then a phone call to Microsoft will sort it for you.
The above applies to the retail version of O/S. OEM versions should stay with the PC, they were first bought for. If for any reason you have an OEM version and because of some sort of major failing of your PC that requires you to buy new, then once again, a call to Microsoft will usually receive a sympathetic hearing. j.