As far as music quality sometimes nothing, sometimes a lot. In general a lot more time is spent on a master from pre-production through tracking, through mixing and then it’s mastered, a step not usually taken on demos.
The big difference is rights in regards to selling the project for profit, which reflects on how many $ are shelled out for the recording. The songwriter(s) fully own the rights to the melody and lyric but the right to sell the recording depends on what the songwriter(s) pays for. If the musicians on the recording are paid demo rate then the songwriters can give away all the demonstration copies (on CD or MP3 usually) they like, but they can’t legally sell it. Demos usually cost in the hundreds.
Paying for a master recording (usually costing in the thousands of $) gives you the right to sell CD copies or downloads. It’s important to be sure the singer (if you don’t sing the song yourself) understands that’s the intent.
Two fairly recent developments passed by the musicians union:
1. A limited release master, cheaper than master rate, allows you to sell up to 10,000 CDs or downloads
2. You can upgrade from demo to master by paying the difference. In the old days a demo was forever a demo. I believe this upgrade became inevitable as demo quality and complexity improved and many demos sounded nearly as good as masters.- b.e.