I'm not sure what difference that is supposed to make in the Trek context, where indeed no difference is made between the two types of Lieutenant, and no flag officer identifies him- or herself by a specific grade of Admiral, in the most formal of occasions. (It is only in relatively informal occasions where the concepts of "junior grade" or "vice" are uttered instead - once or twice in the entire history of Trek.)
If the real-wold examples are not relevant, why bring them up? But anyway, "vice admiral" and "rear admiral" were used in official orders in TNG and DS9.
Two types of Lieutenant Commander or two types of Lieutenant - same difference. Even in courts martial, it seems, which is okay if it's okay for Starfleet.
The court martial transcript is an official record and would include exact ranks. The computer says "service rank," clearly more specific than what one would call someone in normal conversation. What you are saying is Spock and McCoy held two separate and distinct ranks (which titles are never heard anywhere), but according to the court martial transcript, and the computer that read their service record into the transcript, their ranks are the same. I don't find that at all plausible.