Booting internally from a harddrive that was used on a different Mac
What operating system(s) are we talking about here?  If you installed say, a retail copy of Snow Leopard on one machine, then transferred the HD to another machine, that might work.

But if you installed your OS using the disks that came with the machine, those disks are specific to the machine itself: they're streamlined with various drivers and whatnot, is my understanding, and will not work in another machine.

I'd have to read up again in the CCC documentation but I believe there are also instances where files that are hard-coded with UUID's or MAC addresses or something that need to be properly re- created when moving a drive to another machine.