A flat-rated engine achieves rated thrust at sea-level well below the maximum internal temperatures (ITT). Therefore, that same thrust can be achieved to a high altitude before reaching the limiting ITT ("temping out"). Achieving the same thrust output for a good portion of the aircraft's altitude capability is where the 'flat' term comes from from: the thrust output is 'flat' until a certain density altitude, at which point the thrust curve starts to fall away.
A de-rated engine simply lowers the thrust rating achieved at sea-level.
These two terms are not mutually exclusive.