Detector question on lock-in circuits

I see demodulator circuits that to me look like a full wave rectifier, they take an AC signal and flip its negative part above the line. This is the last stage of a lock-in before the integration-cleanup phase.

In situations where you control the light source, I have thought of using square wave pulses, with measurements taken during 'on' and 'off' periods.

It makes sense to me to subtract the 'dark' signals from the 'on' signals, and collect the 'on' signals for DSP.

But some lock-in circuits describe a switching network that essentially does a full wave rectification of an AC signal.

Can anyone explain the difference here?

thanks in advance JB