I have two mac computers, one pro and one mini. I am having trouble with singing-in to Apple with One password. The computer I make it on will sign-in OK but if I try it with the other, it will not recognize it. I am using only one email for both.. W

I have two Apple computer, a Mac Pro and a Mac Mini.. When I attemped to sign in on Apple on one of the computer (Mac Pro) that I made the password on, will work OK but if I got to the other computer (Mac Mini) and sign in, it will tell me I am using the wrong password, so if I go and make a different password for the Mac Mini computer with the same email for both computer, it will work for the Mac Mini computer but not the Pro..

I have even made another email account for the Mini and tried that but it will still go back to the original.. What can I do or need to do to correct this?? Please Help if you can>> Betty