Output voltage of a rectifier
Ignoring diode losses. If you measure the output voltage of a rectifier as the Root Mean Square (RMS) voltage you are getting a reading which reflects the amount of power that the source can deliver as compared to the equivalent DC voltage.

The RMS output of a full wave rectifier is the same as the RMS the original waveform. The squared bit removes the effect of half of the original waveform being negative giving the same answer.

The RMS output of the halfwave rectifier is half the value of the original waveform. The mean bit of RMS means you are taking the mean over a full cycle and you only have half of the original waveform there.

Things change if, as normal, you put a capacitor across the output of the rectifier then you get DC. In this case the capacitor charges to   √2 times the input voltage, this is the peak of the input.

If you take a load current from this arrangement you get a pulsating DC voltage. The pulsations value depends on the frequency the size of the capacitor and the current. This is well documented in other questions. See this question.