It's pretty similar, from the point of view of the purpose it serves for "hedging" customers. It's an insurance against default by the borrower, which repays you of the nominal remaining at the time of default (forgoing expected trailing interests, but you can reinvest the premium at the rates available at the time).

And the cost is regular payments, so it really works a lot like those "unpaid lease" insurances that individuals can get for property they let.

But it is different from an asset-backing, in that it is hassle free: you get cash, full stop. No legal action to take to seize the backing asset, no doubt about its future value and liquidity at the time of default, no delays...

The two can coexist: there are CDS on asset-backed loans. But you can't have your cake and eat too. In such cases, the CDS contract says that all you initial entitlements as lenders are transfered to the CDS issuer (that is, they try to recoup the loss they made on a default, by snatching the assets and getting whatever recovery they can - in short, with the CDS, you transfer the hassle to a bank)

Pierre