they do have the same serial, it just seems a very odd question to ask.
I'm sorry you feel like this is a odd question but honestly if you had mentioned that at the beginning of this topic you would have not received any assistance because what you have is a illegal installation of the OS. The registration number is for one system only when you purchase the media with the registration number.
The TOU clearly states that and since you were also getting assistance from another site at the same time and they were able to help it has resolved the issue we started here.