In a really nice paper, a Honeywell engineer explains all the terms and how they came to be as FMSes evolved all the way to the 777.
A general FMS evolved from combining RNAV (Area Navigation) and PMS (Performance Management Systems), lateral-only and vertical-only navigation computers, respectively.
An FMCS has two basic components or boxes: a CDU (the pilot's interface) and an FMC (the actual computer). A typical installment will have two of each crossfeeding into each other.
Starting with the 777, FMCs are no longer discrete boxes, see: What is the difference between FMCF and AIMS on the 777?
An FMS will consist of the FMCS, and the interfacing components: EFIS (Electronic Flight Instrument System), auto flight, and auto thrust.
An MCDU, or Multi-function CDU, includes additional functions via the ARINC 739 interface:
- Central Maintenance Computer
- Backup functions when all FMCs have failed, e.g.:
- Standby navigation and lateral guidance; the MD-11 and 777 also allow coupling those to the separate auto flight system
- Backup EFIS control (e.g. 747-400 and 777)
- Backup EICAS display (e.g. 747-400)
Interestingly, the 747-400's and 777's flight manuals use the term CDU, owing to the basic CDU of the 767, despite being MCDUs according to their manufacturer.
That leaves us with FMGS:
The FMC "box" of the A320-family includes cards made by Sextant Avionique (now Thales) for the flight director, auto flight, and auto thrust, all in one unit, hence the G for Guidance and S for the all-in-one System.
In the Honeywell family, the Boeing vs Airbus relation is more of a software one:
Internally (Honeywell), they are referred to as Brown (Boeing) and Gray (Airbus), based on the cockpit colors. The MD-11's basic architecture is Gray (as shown above), but with added Brown system functions, for example:
The Gray systems provide for an Active flight plan and a Secondary flight plan. On most Gray systems, when the Secondary plan is activated the previous Active plan is deleted, but on the MD-11 systems the old Active plan becomes the new Secondary plan.
A notable but long forgotten acronym is AFMC (A for Advanced), where solid state memory replaced the ruggedized hard disk drives, which were the only option with "adequate speed and capacity" back in 1978 when the development started.
Liden, Sam. "The evolution of flight management systems." AIAA/IEEE Digital Avionics Systems Conference. 13th DASC. IEEE, 1994.