All of the officer ranks above get a mention - except for "sub-lieutenant" (which in USN parlance is "lieutenant junior grade") - this rank only gets indicated by its very own sleeve braid in TOS (the minor role of Joe Tormolen) and its very own pips in TNG, DS9 and VOY (several major roles such as Worf, Julian Bashir and Tom Paris).
Also, there is a "Fleet Admiral" in TNG era parlance, but that title apparently isn't tied to any specific rank - it is commonly associated with the three-pip rank of Vice Admiral. The five-pip Admiral rank does not make an appearance in the TNG era. A rank higher than Admiral does appear in the TOS movies, but is not given a formal name; people wearing this rank pin hold positions such as "the CinC" or "Commander, Starfleet". One might surmise Starfleet does have a name for this rank, and further that it won't be Admiral of the Fleet as this would cause confusion with the job title. Grand Admiral, perhaps?
Beyond this, Starfleet ranks and USN ranks are a very close match overall.
Enlisted ranks or ratings are a different matter. Only the TOS movies have featured a comprehensive scheme of pins, and even that was in no way as extensive as the USN one. Dialogue confirms the existence of Petty Officers, though, and O'Brien's rank tends to feature the word Senior, suggesting commonality with the USN rank of Senior Chief Petty Officer. This is about as specific as it gets, though. There are "crewmen", but that might be a position rather than a rank; there are "yeomen", and that probably isn't a rank, either. And then there's Crewman 1st Class Simon Tarses, suggesting the USN thing about every rating having three sub-ratings (Crewmen 3rd through 1st Class, Petty Officers 3rd through 1st Class, and then this Chief Petty Officer / Senior Petty Officer / Master Petty Officer trio). Our only real TNG era enlisted rank indicator, O'Brien's collar plate, supports the idea by featuring three chevrons and space for three stars.
Likely not "spaceman", either, though.
Timo Saloniemi