UST beads ‘lock’ to the rim wall, so they’re a very good fit on the rim. They’re expensive, and true UST tyres are heavy.
There’s been a raft of LUST/Tubless Ready/2Bliss tyres in recent years which have tubless beads, but lightweight carcasses, necessetating the using of sealant (which most people did anyway).
Many brands of ‘normal’ tyre (Schwalbe and Maxxis most notably) will actually work very well anyway, although 2011 Schwalbe Evos have tubeless beads. Some won’t (notably Panaracer) the bead just isn’t a good enough fit on the rim and is prone to blowing off.
To ensure compatibility a UST or Tubeless Ready tyre is the safest bet. However a bit of research and careful selection means that normal tyres can work as well, whilst generally costing and weighing less.
I personally use older Schwalbes, have about 5 sets, all will go straight up with a track pump and stay up.