The Type B was a technically more advanced version of the Type A.
The Type C was a straight-4 engine derived from the Type A.
Many parts were interchangeable between the Type A, Type B and Type C engines (e.g. pistons, valves, rods). Many of the same parts were also interchangeable with the Chevrolet Stovebolt engine, from which it was derived.
The Type E was a copy of a DKW engine.
The Type S was a straight-4 engine that replaced the Type A, B and C in Toyota's passenger cars.