My understanding is any British ship with the label “RMS” was special. It was a ship the British government deemed suitable to carry mail which lent that ship a notion that it was fast and well run (safe…and I think Titanic was a “RMS” so…yeah, not a foolproof thing).
Does that designation sill exist today for ships?
There are currently three ships in service with the status of Royal Mail Ship. Only one of them, RMV Scillonian III, actually carries mail along with being a ferry between the Isles of Scilly and the British mainland. The other two are RMS Queen Mary 2, the only operating ocean liner in the world, which bears the title ceremonially in homage to the original Queen Mary, and RMS Segwun, a Great Lakes steamer from 1887 that is now used for sightseeing tours in Muskokwa, Ontario.
I think the RMS prefix just denoted that the Royal Mail had a contract with the operator of that ship for it to carry mail, and that the award of such contracts was at least partially driven by commercial considerations, such as the price the operator would charge for that and the need to have additional resources on that route. I don’t think it was necessarily a seal of approval of a ship’s particular quality.
Facilitating international communications [mail, telegraphy and eventually telephone] was a big deal in the 19th century so while RMS might not confer particular privileges, it did signify that the ship had some sort of vaguely official obligation to not be unnecessarily delayed or messed about with, or words could be had a governmental level.
Until the recent construction of an airport on the island, as I understand it, St. Helena was serviced by an RMS vessel every month out of S. Africa. It was apparently the only way to book passage to the island. Though non-scheduled ships and fishing vessels called regularly. From wiki: " In 1989, Prince Andrew launched the replacement RMS St Helena to serve the island; the vessel was specially built for the Cardiff–Cape Town route and featured a mixed cargo/passenger layout." The airport was completed in 2018.