Unlinking my computers

So migration assistant was used to set up my new MacBook Pro - as much as I understand - but now anything that I change on my new computer changes my old computer and vice versa.

How do do I stop this? I need them separated!! My old computer is starting ™ I fail but I cannot start using my new one until I can set it up and I need to know if I go back to factory settings in my new one but f it will also erase my whole life on my old computer!!