The OD-880 is labelled "Overdrive" with "Soft Distortion" below.
This is an op amp distortion that uses a pair of back-to-back silicon diodes for passive clipping.
A non-inverting input buffer amp is followed by an inverting high gain amp, then passive clipping, then a x10 inverting make up gain stage, probably to correct for the inherent output limiting of the passive clipping stage. Overall phase in in-phase from input to output.