What is the difference between the round and square air cleaners? Square seems the predominant style. Are they time frame/ manufacturer/engine type specific?

You might find your answer here-

http://the.shadock.free.fr/sherman_minutia/

They were interchangeable for M4 and M4A1 tanks, and just reflect different vendors for the part. PSC seems to have used the round type pretty commonly on their M4 and M4A1 production. If this is maddeningly vague, remember that most photos are taken from the side or front, and that the area in question is heavily shadowed in the available pictures. As with the top run track skids, these parts are often completely invisible due to heavy shadows.

Thanks, Gerald. It'd looked onSherman Minutia and they don't really give any hard set rules (not that there are many with Shermans.) Most photos I've seen seem to show the square. Like you said, not many clear shots of the rear. Plus at some point in time they started adding armor plates to protect the air filters , hiding them even more.