I’ve seen these two phrases bandied around. And read posts about running tubeless. But what is the difference? I still have inner tubes on all my bikes. Is tubeless “better” than going with inner tubes?

Yes it is better.
UST (universal system tubeless) is mavic’s tubeless system – one of the earliest and features v sturdy tyres that are designed to go with mavic UST tubeless rims, although they will fit any rim. I used this set up for years and it was super reliable and simple at a time when other systems were not.

Seen as they got it basically right the first time, Mavic didn’t put much effort into developing UST (except at the top levels), so they have now been overtaken by other competitiors (Stans is prob the most widely used) who offer set-ups that feature lighter rims and lighter, cheaper tyres. These are the TLR tyres you mention which work just the same, just lighter and less expensive.

Though after frequent blow offs I’ve just put a tubeless tyre on my back Flow Ex. Admittedly on my most aggressive bike. Will be interesting to see how I get on with 29er XC tyres in a month or so’s time.

Front’s been fine with a single ply, bog standard HR though. So as people have said in other threads, its tyre:rim combos which can make or break the success.

Never thought much of tubeless until I discovered ust RQ’s

It is better IMO. Punctures are psychic, they wait til exactly the worst possible moment to happen, the dicks. Tubeless can be faffy, but it’s faff in the garage with the radio on, rather than faff up a mountain with a thunderstorm on.

The major difference between UST and Tubeless Ready is that UST is supposed to work without sealant, TLR isn’t- the beads are designed for tubeless but the tyre may not be airtight. In practice most people use sealant with UST anyway so it’s a non-difference most of the time.