You are mixing up different literary theories.
The concept of the hero comes from a view on literature that is derived from ancient epics. The concept of the protagonist is derived from Greek drama theory.
What is importatnt here is that the hero and the protagonist have nothing to do with each other. They are different approaches at trying to understand how literature works.
A hero is a figure undertaking a quest (Odysseus). Not every narrative has one. The hero's journey is about self-discovery and self-development. He is not necessarily up against anything (Hydra is not Hercules' opponent but a task he has to complete). A hero acts in the context of fate and divine forces.
The protagonist is the primary actor. By default, the hero is the protagonist of his narrative. But a protagonist is not always a hero. He may be fighting an antagonist that is on the same level as he and, unlike fate or the Greek gods, can be overcome.