More or less. Since we somehow don’t seem to have a Trekker with encyclopedic knowledge of Star Trek participating in this thread, here’s my memory/understanding:
In TOS, there were, as someone upthread put it, “smoothsleeve” crewmen, which might seem to indicate the existence of enlisted ranks, but that wasn’t firmly established, and Roddenberry himself said that everyone on the ship was an officer.
Dialogue in the show established the existence of the ranks of Ensign, Lieutenant, Lieutenant Commander, Commander, Captain, Commodore, and Admiral. Going by the pattern of rank insignia on the sleeve cuffs, we can interpolate the existence of a Lieutenant, Junior Grade rank, but that’s never mentioned in dialogue, and I don’t know if we actually see characters with that rank insignia. That’s actually a slightly anachronistic version of USN ranks (the contemporary USN no longer had “commodores”).
There’s also a “Yeoman”, but that seems to be a position rather than a rank, and a “Fleet Captain”, but it’s entirely unclear if that’s a rank, a position, an honorific, or what.
In the TNG era, ranks are rather clearer. Between dialogue and the pip rank insignia, there are ranks of Ensign, Lieutenant (Junior Grade), Lieutenant, Lieutenant Commander, Commander, and four grades of Admiral. Everyone with a “pip in a box” is addressed as and referred to as “Admiral”. I don’t know if we actually saw every grade in the show, but we did see “Admirals” with different numbers of pips in the box, up to four I think, which implies four grades of Admiral, as in the USN, but apparently without separate rank titles.