Half wave vs full wave rectifier
The 4 diode bridge is a full-wave voltage doubler and achieves 200% of the voltage and 50% of the current of the centre-tapped 2 diode full wave version.  Thus the tapped version has lower impedance.

Some users might consider the tapped 2 diode version as a 2 phase each half wave combined to make a full wave.  But in fact, the secondary is only a split-single phase.

A half-wave bridge is a single diode version is used  when less  voltage and current is needed and thus the longer charge interval is adequate.