How can I best describe this phenomenon (I do need a brief term). Would "differential style" be OK? or should it be plural ("differential styles")? or something quite different such as "style differentiation", or "differentiated styles"?
You could say that the author has a protean style, where protean means something like "versatile or changing depending on circumstance".
Or you could say that the author's style was context-sensitive, meaning "sensitive to context".
Colloquially, "changing hats" can fit this context. It refers to changing one's role in a situation as one would change wearing apparel when performing different tasks. Alternatively, if you can substitute another word for "style," there would be more options for expression. Examples include "adapting to different audiences" or "varying his approach for different settings."