Kiraly is correct, that they should be the same, but that won't keep TM from backing things up (it could, however, give you fits when restoring, so by all means change your TM drive to be the same as your internal HD).
So, there's something else going on here.
Are you running File Vault?
What happens when you do a backup? Does it fail? If so, start with the
Time Machine - Troubleshooting *User Tip* at the top of this forum.
It will show you how to locate the message(s) that describe the problem, then help you fix it.
If that doesn't help, post back with details, including all the messages, your setup (especially the destination for the backups), what you've done, and the results.