The 'synthetic' means that the issuer may not (and most likely does not) hold the risk being tranched (loans in your example). Instead it generates return by selling CDS protection on certain market defined risks (hence the word synthetic, in the sense of being a derivative exposure).
This makes a big difference:
1. Since individual tranches can be created on demand (unlike a regular CDO, where the full capital structure has to be placed), banks can create bespoke standalone tranches which are then hedged based on a correlation model. Thus there is much lesser market feedback to put a brake on unbridled issuance. A (very) loose analogy would be insuring your house (i.e. needing to own the loan under the CDO) and betting that your neighbour's house will burn down (where you have no skin in the actual asset). You can clearly do much larger sizes of the latter contract, for the first one, you need to buy a house each time you want to put the trade on.
2. The CDO invests in collateral to back the protection sold. One of the issues during the crisis was that this collateral itself was other CDO tranches (either synthetic or physical). When the market melted down, these assets became unpriceable given the opacity of the collateral. Result = even higher illiquidity
Of course the issued size is nowhere near becoming a systemic problem similar to 2007, but it does seem that those who do not learn from history are condemned to repeat their errors.
In this context Raghuram Rajan's speech at the 2005 Jackson Hole symposium is especially prescient: https://www.imf.org/en/News/Articles/2015/09/28/04/53/sp0827...
Edit: misread JumpCrissCross's reference to payment processors as protection buyers, deleted this part.