I think I understand the difference between esoteric (my opinion) and exoteric (this is what I think the world is). What is the difference in writing style dict

I think I understand the difference between esoteric (my opinion) and exoteric (this is what I think the world is). What is the difference in writing style dictated by the two different types of claims, though? Neither reading that wiki page nor quick googling helped me find examples of the two different styles.