First of all, having the OS and your data on the same physical drive is not wise.
And backing up to a different partition on the same physical drive is only marginally worse than not backing up at all. Fried drive, corrupted MFT/MBR and bye-bye data forever.
Backing up to a different internal drive on the same drive controller isn't much better, for the same reasons.
Backing up to a removable drive (caddy or USB) is good, but a raw machine readable copy, rather than a backup compressed in some proprietary format that needs the OS and backup program reinstalled is much more flexible.
Imaging the drive to a removable drive is OK, but you must be sure of the integrity of the image. A corrupted image may well lose the lot, rather than just a few files.
I have about 10,000 irreplaceable images (and other stuff) on my main machine's data drive and multiple backup strategies.
1) I do an incremental copy of the data drive to a caddy removable drive that spends most of it's time at work (20km away). This drive gets copied to the work machine when I get there and is stashed away in another part of the building until next time.
2) I have a separate machine hidden away at the far end of the house in a locked cabinet with a fat UPS. This runs FreeNAS (a BSD Unix variant) and the main machine backs up in real time to the primary disk on this machine. The primary disk does a weekly rsync to a secondary disk on this machine and the secondary disk does a monthly rsync to a third drive.
I don't think backing up the OS drive is helpful. If the OS gets hosed or is somehow compromised you'll never know what is reliable. The best restore is a full reinstall.
Paranoid? Sure.
Have I ever lost any data to mechanical or software failure. Not yet.
Mac