Relationship among passwords

I have an Apple ID and an associated password. I understand that this combination identifies the Apple user, rather than the device that the user uses. I also have a Mac mini and a Macbook Air, each of which has its own password for accessing the user interface. I want to change the passwords for the Mac mini and Macbook Air without changing my Apple ID or its associated password. Some information that I've read suggests that this is not possible and that changing the Mac mini (or Macbook Air) password might result in the password associated with my Apple ID changing. Is this true, or are all the passwords independent of each other?