There are a lot of names for this type of transaction.
The most accurate (imo) is rent-to-own.

The buyer does not own the property until he pays up fully.

The issue, of course, being that certain types of title changes have precedence and wipe out the rto contract (along with the down and all payments previously made).

To protect yourself you would want language clarifying what happens in the case of mortgagor distress (though that would still be very thin protection at best).

Better would be a very specific type of trust deed against some other collateral this seller has that only kicks in if your rto interest is compromised or eliminated.

The price point for that type of property varies wildly depending upon which areas you like.

These contracts are pretty rare in SD (or any place with lots of foreclosures).

You also want to clarify what happens if you move prior to the transfer of title.

The outline you have given really sounds more like a lease with a $20000 option to buy.