The FMS (Flight Management System) is made up of 4 parts.
1) FMC (Flight Management Computer)
2) Autopilot and Flight Director System
3) IRS's
4) Autothrottle System
Each part can work collectively or independantly.
FMS is the term used when combing all these components to work together to make up the Flight Management System as they are all the systems used to obtain performance data and to fly and navigate the aircraft by automation.
So the Flight Management Computer (FMC) is just a part of the whole FMS.
Hope that helps and I describe as per 737 aircraft. Airbus use differnet terminology (FMGS) though I think the logic is the same.