The Perelandra Boost / Overdrive is a recreation of the Xotic BB Preamp, a flexible tone machine that lets you go from a clean volume boost to a nice smooth overdrive with a 2-band EQ to shape the tone.
The BB Preamp is very similar to the Ibanez Tube Screamer, but with an active Baxandall tone control added before the output buffer so that the treble and bass can be independently boosted or cut.
In fact, if you look at the schematic for the BB Preamp, you can see that the original Tube Screamer tone control stage is left intact, but with the tone knob is fixed at 5% rotation (i.e. almost fully to the dark side of the control) by using a 1k and a 19k resistor. The main difference between the BB Preamp and the AC or RC Booster is the presence of this Tube Screamer tone control stage to shape the tone going into the Baxandall EQ.