What's the difference between FMS and FMC?
(Own work)

The FMC is part of the FMS.


  The FMC is a computer system that uses a large data base to allow routes to be pre-programmed and fed into the system by means of a data loader.


The FMS encompasses:


  
  The Flight Management Computer (FMC)
  The Automatic Flight Control or Automatic Flight Guidance System (AFCS or AFGS)
  The Aircraft Navigation System
  An Electronic Flight Instrument System (EFIS) or equivalent electromechanical instrumentation.
  




Further reading: Flight Management System (SKYbrary)