H-Bridge

An H-Bridge is an electronic circuit that allows a voltage to be applied across a load, usually a motor, in either direction.

This bidirectional control of current enables the motor to spin forward or reverse, which is essential in many robotics and automation applications.

Half H-Bridge

A Half H-Bridge is a simplified version of the full H-Bridge circuit. It controls the flow of current through a load in only one direction (instead of two) and typically consists of just two switches (often transistors or MOSFETs) rather than four

This is from the Allegro A3901 diagram.