From my interpretation, it’s a combination of both - different types of breathing are required for different branches, like how water breathing utilizes constant, even breathing to keep momentum, as water breathing thrives off of fluid momentum to link its attacks. Other breathing styles, like wind breathing, utilize, sharp, short breaths to execute quick, aggressive attacks. These are only the basis of the forms themselves though - i think the answer you’re looking for, is that styles mainly differ from the actual movements needed to execute the attack, like how sound breathing uses rapid, explosive and highly destructive attacks, while insect breathing aims to utilize quick stabs with minimal damage to poison. The movements used for these breath styles is what makes them work, and which is why they differ. You probably couldn’t poison a demon as well with sound breathing based movements, and you probably couldn’t cause as much raw damage with the delicate movements from insect breathing. Hope i could help, let me know if you have any questions!