Not only awakening gives it's user a new form it also influences them
I know how awakening works. For zoans the only thing that was stated is “their physical strength and recovery rate increases“ based on the thinks we have seen mythical zoans are different because each of works differently and the awakening can be unique. Kaidos zoan works very normally to other zoans except the special abilities that it grands like fire breathing, dragon clouds, twisters, etc.
marcos functions like a logia and gives healing abilities.
Luffy’s abilities work like a paramecia.
I‘m gonna give you an example: in dragon ball at the beginning you could tell the difference between Ssj and Ssj2 but later on it was almost ambiguous.
haki at the beginning you could tell when it was used due to the black coloring. Later on it got ambigues.
awakening is the same at the beginning it is shown and metioneds and later on it becomes more normal.