25 years ago I wrote a brief for my management explaining the distinction between "reduced" and "derated" thrust - it's essentially that derated ops are based on actual flight test data, whereis ATM reduced thrust (FAA Order 8000.39 applied in those days) involved some conservative extrapolation, and thus additional conditions applied. (For my sterling efforts, I received a pink slip; they shot the messenger)
For maximum operational flexibilty, an operator should have both protocols available.
The current document is FAA Advisory Circular (AC) 25-13; I haven't explored it in great detail, but I doubt it invalidates the prior order.