i.e. the booster doesn't know it's actual position to within 0.5cm but it knows it's position relative to a buoy or the catch arms to that precision.
But survey grade gnss is a web of rabbit holes, if you want to get into it.
And there are ways to get sub mm accuracy both relative and absolute, but idk of one that would be quick enough for the required reaction time of dynamic landing via 'catching'.
But multi-centimeter (4-5) that's really easily doable is probably good enough for other systems to take over from.
[1]: https://www.youtube.com/watch?v=pAPt5vbr-YU (don't recall timestamp, sorry)
GNSS is more than accurate enough once you know all slight errors in satellite orbits and the atmospheric distortions currently affecting the area near the base station and can correct for them.
Or in fact, you need even better than that, since you don't want your whole error budget used up by the GNSS system.
No reason you couldn't use RTK GPS for <10cm accuracy for most of the flight, then in the last few meters of landing switch over to to high-precision, short-range tracking - like optically tracking a marker on the grabbing arm.
For other specific cases - like bridge monitoring - there are reports of 2–3 mm precision [1]. Of course, bridge monitoring has quite distinctive requirements; a 5Hz vibration component and a 0.0001 Hz thermal expansion component. So there's a lot of potential to average over lots of readings to reduce noise.
[1] https://www.sciencedirect.com/science/article/abs/pii/S02632...
The earth's crust floats on top of liquid rock. This matters at relevant length and time scales; in most places, these effects alone are on the order of millimeters per year. One reason why it's better to use NAD83 over WGS84 in North America is that NAD83 latitudes and longitudes move with the North American plate.
Positions _are_ relative, and the closer you can put your datum, the less drift you'll accumulate.