What is the use of fast diodes vs rectifier diodes?
Diodes conduct some time also to the reverse direction when the diode at first was conducting to the forward direction and the voltage is reversed.

Fast recovery diodes are optimized for fast turning off when the voltage is turned from forward to reversed. Its needed in switch mode power supplies because generally the time when a diode conducts to the wrong direction cause losses. The same is true in circuits which convert DC to AC.

Rectification diodes which are used at 50...50Hz are not optimized for fast recovery, but for low losses in forward state. The voltage drop for forward current has been tried to be kept as low as possible. The recovery time can be several microseconds, but that's not catastrophic with 50...60Hz sinusoidal voltages. The unwanted reverse conduction happens sparsely when compared to SMPS which has 1000 times higher frequency and the sinusoidal voltage grows slowly when compared to pulses in SMPS.

If you put say a 1N4001 to the flyback pulse circuit in SMPS instead of a recommended fast recovery diode you can see radical increase of losses. Input current rises and parts run hotter because the reverse conduction time means a short circuit.

In radio circuits there's one more use for fast recovery diodes. The ending of the reverse direction current is possible to be made so abrupt that with properly designed resonant filters one can extract higher frequency sinewave (=a harmonic) with remarkably high efficiency. The idea is used commonly in microwave frequency multipliers.