A flat-rated engine is an engine, which produces the same amount of thrust regardless of temperature from a certain temperature point (around ISA+15 for most engines).
A derated engine is an engine, that has been modified (this modification can be very simple - depends on engine/airframe) to always produce less thrust than what it was designed for. Reasons for this may be better (smaller) noise footprint, reduced maintenance cost, increased EGT margin, reduced VMCG/A, ... On some aircraft you have an option of a fixed (permanent) derate, which requires maintenance action and a "semi-fixed" derate, which can be selected by flight crew to conform the operational needs.