The assets that back the bonds called asset-backed securities (ABS) can be basically anything with a fairly predictable cash flow, but debt repayment cash flows tend to be used the most. These include credit card debt, home equity loans, auto loans, student loans, and so forth.
When we think of ABS, we tend to lump them together with Collateralized Mortgage Obligations and Mortgage Backed Securities. If we constructed a taxonomy or hierarchy of such securities, MBS would be a subset of ABS, in theory.
In reality, because the mortgage-backed securities came first and may even have specific rules and legislation which shaped them before similar securities appeared on the scene, these categories remain distinct. Interestingly, the bond notes known as Collateralized Debt Obligations are considered distinct from ABS as well since they are just downstream.
CDOs and CMOs take their upstream counterparts of ABS and MBS, pool them once again, and divide them into tranches, and sell off the various classes of shares. Asset-backed securities themselves can be tranched, but alone they have a higher prepayment risk than the larger pools of CDOs or the more insulated PAC instruments.
They are pooled and divided into tranches in the CDO — and that is only if they meet the criteria to be included in a CDO. Some asset-backed securities use cash flows from the royalties of creative works (movies, books, etc), accounts receivables for a business, or various other non-debt sources. Asset backed securities sometimes have payments secured by insurance contracts known as financial guaranty insurance.
Plenty of theories are known because they are useful, and it is up to you to discern which ones may be worth your time
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