These two terms are often intermingled and interchanged to the confusion of some.
Basically their are 3 ways the engine is controlled.
1) The very basic, strictly mechanical (cables, rods etc) interface between the throttle and the engines fuel control unit (I'll use the term fuel control unit or FCU as the generic fuel metering device that controls engine thrust and other related functions).
The FCU itself is a very complex hydromechanical RPM governor that utilizes engine RPM, engine pressures and temperatures to control engine thrust to the desired power setting selected by the pilot moving the throttles.
This system has few safeguards to prevent the overtemping or overspeeding of the engine.
Plus, the throttles must be adjusted to compensate for temp, barometric pressure/altitude changes to maintain a constant thrust.
2) Supervisory system controls: The next step up are engines with supervisory control capability (737-300, some 757 & 767's, some A310 & A300-600's). Essentially this system is an upgrade of the basic cable, rods and hydromechanical FCU and puts an electronic engine control in the mix. This engine control will fine tune the engines N1/EPR (though its authority is limited) to a steady thrust during changing conditions (climbs, descents etc). This system offers more exceedence protections and monitors more engine parameters than the basic hydromechanical FCU.
The control box is referred to as the EEC (electronic engine control) by RR and Pratt? And PMC (power management computer (control?) by CFM.
3) FADEC: This system is the latest and most sophisticated. FADEC is essentially engine control via "fly by wire". Their is no mechanical connection between throttle and fuel control. The heart of the FADEC system is the EEC (Pratt) or ECU (engine control unit/General Electric).
Sometimes its best to understand this system in a way you can visualize. Imagine in your living room, the light bulb is the engine and the dimmer switch is the throttle. Moving the throttle forward is equivalent to turning the dimmer switch toward brighter. The difference being is with FADEC the dimmer switch goes to the ECU/PMC and they act as the middleman with lots of inputs to control the engine with far greater precision than old basic system or the supervisory system. This system has protections to guard against overboosting or overtemping (during start on some aircraft). But the main protection is the precise manner in which the engine is controlled and monitored by the EEC (PW) or ECU (GE).
You're only as good as your last departure.