ASX listed CFDs are actually listed on the exchange. Not a bad idea, and more transparent, but no-one seems to want 'em and they have miserable liquidity, which kinda defeats the purpose.
Synthetic CFDs are what almost everyone uses, and are essentially bets against a CFD provider. They are usually pegged to the actual market action (so if I buy 1000 ABC at $1.05, my CFD can be filled when a number of ABC shares actually sell at that price - depending on the policy of the CFD provider).
OTC are purely synthetic - they are a direct bet against the CFD provider. You put in that order for ABC, but nothing shows up on the exchange, and you're filled when the provider's policy says you're filled. Note well that their policies are generally pretty dodgy, since part of their income is you losing money. (Example: some maty not give you your ABC when ABC sells in good volume at your price, they give it only when there are actual Sells listed in the exchange at the price. Or they'll let you put in a trigger price, but force your order to go in at Market, instead of Limit).
DMA CFDs are the other kinds, and are usually traded direct in the exchange by the provider - that is, when you order 1000 ABC, you'll see an order for 1000 ABC go on the exchange. That's your provider buying the position. So the fill is exactly as if you'd placed the trade yourself. DMA is more transparent, then, but you pay in higher brokerage, worse margin (though still more than enough for most people to lose all their money), more limited markets, and - crucially - higher interest payments. With most CFDs, you pay interest on the entire position, regardless of the deposit, so it really adds up.
So there y'are. Not synthetic: ASX listed (awful liquidity). Synthetic: OTC (bad fills, lots of slippage) and DMA (higher fees, less range).
...and the ASX listed are such a tiny part of the market, you can generally assume people are talking about the other kinds.
(For the record, I use OTC mostly, even though they're dodgy crap, because I like the variety of markets and sometimes need the extra margin. I get a lot of signals and like to take as many as I can. You just need to learn the particular dodgy bull**** your provider employs to rip you off, and work around it. That, and be flat out terrified of the margin, and make sure and doubly sure that you're covered against a disaster).