The word “manage” is related to the term “control.” It’s a type of control, specifically operational control. Managers are focused on their control of the organization.
Coaches have control as well, of course, as management is part of their job. However, the origin of the verb “coach” tells us something about what coaches do. The word “coach” comes from a term meaning “to tutor.” A tutor, of course, is someone who teaches another one-on-one, who focuses on helping the other person learn the skills to achieve success.
If what motivates you throughout the day is making sure everything goes your way, then chances are you’re a manager. If, however, your chief concern is helping your team succeed, then you’re a coach or on your way to being one.