Quite right. And while flex, assumed temperature or reduced take off thrust (all meaning the same thing) can be up to 25% reduction a combination of derate (fixed lower thrust rating) and reduced thrust can be more than 25% reduction.
For example on the 737-800 you have full rated thrust of 26k lbs and two fixed derates of 24k and 22k. You can reduce each of the derates further by up to 25% using the fixed temperature method. The fixed climb derates (climb 1 and climb 2) are based on full rated thrust which means you will most certainly get higher thrust when reducing from take off thrust to climb after using derate 2 and a higher assumed temperature.
When using a fixed derate like this you have to be aware that they also impose different base performance data like different Vmc speeds.