Rear Admiral Donaldson
Rear Admiral, Upper Half Insignia
Rear Admiral, Lower Half Insignia
Rear Admiral is a Flag Officer rank used by naval organizations, traditionally between the grades of Captain and Vice Admiral. This rank was used by the Federation Starfleet (as well as its predecessor the Earth Starfleet). The current system uses two tiers of rear admiral rank, "Rear Admiral, Upper Half" and "Rear Admiral, Lower Half." Officers of both tiers are simply addressed as simply "Rear Admiral".
It is generally regarded as the lowest of the "Admiral" ranks, which are also sometimes referred to as "Flag officers" and/or "Flag ranks". In military parlance, is it acceptable and normal to refer to a Rear Admiral simply as "Admiral" in most forms of address.
This rank originated from the days of Naval Sailing Squadrons and can trace its origins to the English Royal Navy. Each Naval Squadron would be assigned an Admiral as its head, who would command from the centre vessel and direct the activities of the squadron. The Admiral would in turn be assisted by a Vice Admiral, who commanded the lead ships which would bear the brunt of a naval battle. In the rear of the Naval Squadron, a third Admiral would command the remaining ships and, as this section of the squadron was considered to be in the least danger, the Admiral in command of the rear would typically be the most junior of the squadron Admirals. This has survived into the modern age, with the rank of Rear Admiral the most-junior of the admiralty ranks in Starfleet.
When formally introducing a Rear Admiral, it is proper to use the full rank. However, in most other situations, it is expected to refer to them as "Admiral." In some cases, especially with inferior officers, it may be highly offensive to do otherwise.