The gist of the STO/ABT constructions is that actual assets, be it debt, equity, or what have you, are backing the token. Real (future) cash flows back the token created out of thin air. These can represent REITs, Accounts receivables, debt, VC or really any cash flow coming from the real world.
To make things clear, and in an interesting parallel, we will describe FIAT money as an ABT. This is not a stretch or abuse of language but rather a factual staple of modern monetary theory (MMT) and a illuminating meditation for those that wish to spend some time on it.
All FIAT money, at least in the west:US/EU/JPY, is BIRTHED AS DEBT. What that means is that we create the token representation we call the dollar out of thin air in the banking system. It is a token which is worth ZERO at birth for it came out of nothing. It is however backed by debt, meaning that the new emissions are linked to debt repayment at least for those circulating in the economy (as opposed to the abstract QE for banking which was just patching balance sheets in 2009). A token emitted in the economy needs to be repaid in full (plus interest). The interest does not interest us here, bad pun aside, and it is the principal that we focus on. Once the debt has been repaid, the token actually represent A REAL DOLLAR FROM THE REAL WORLD for it has created it's own value in real life and has created the corresponding cash flow.
In the parlance of the stable coins, the dollar is backed 1:1 via debt repayment.