The disks also have to be the same.
Ummm, I don't see why. The drives can be completely different, or just separate partitions.
The bigger problem in my mind is the legality of this. It is most likely your copy of XP is an OEM license - that is, the Windows license came with, or was bought for the old computer and in that case, you can NOT
legally transfer it to a different computer.
If no original disks came with the XP machine, it is an OEM license. If you have the original Windows XP installation disk and it is “branded” with a computer maker’s brand name, or is labeled with “OEM/System Builder”, “Upgrade”, “Academic Edition”, or "For Distribution with a new PC only", it is not
transferable to a new PC (or upgraded motherboard) under any
circumstances. These OEM licenses are inextricably tied to the "original equipment".