With specifics depending on aircraft, generally the following applies:
FMC - Flight Management Computer
FMS - Flight Management System (consisting e.g. of two FMCs)
MCDU - Multi-Purpose Control and Display Unit (2 or 3 installed on the aircraft, the screen and keypad unit by which the crew interfaces with the FMS)
Airliners have all of the functions provided by the boxes above, although depending on setup sometimes some of the computers are called differently or are unified. E.g. on Boeings, it’s called a CDU not MCDU, and some retrofit older airliners have an FMCDU which is an MCDU with a built-in FMC.
Of course crew learn how to operate these systems.