IPad – iMessage and FaceTime account wrong

The short answer - you can either call a phone number (iPhone + FaceTime) or an AppleID (iPod/Mac/iPad + FaceTime) and you can't call another device with the same number.

To call back to your mac (or any other AppleID device) - you'll have to make a second account with a different Apple ID. Similarly - there's no easy way to get the phone number into another device since that gets authenticated over SMS in the background and not user/password for AppleID.

If you are calling from an iPhone - you can call your AppleID devices (they all ring and any one can pick up), but for AppleID based calls - you need to call a different AppleID unless Apple ever changes the current software.

Last clarification - AppleID is just a string but most people use an email address since that is more likely to be unique to one person.

I believe this is associated with automatic downloads and/or iTunes Match. See http://support.apple.com/kb/HT4627

Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days.

This article makes it sound like you can only sign in with a different account every 90 days, but this doesn't seem to be the case in my experience. I regularly sign into different accounts on our family's iPad when downloading apps and this has never been a problem.

I've only gotten warnings regarding this 90-day lockout when enabling iTunes Match.

The article also notes that:

Note: Removing a device from your Apple ID does not override the 90 day timer. The timer must complete 90 days from the day the device was associated before it can be associated to another Apple ID.

It looks like you'll have to contact Apple if you want to have the device reset.