"differences between actual and apparent authority"?

Answer 1

Form it as a question next time. Everyone has apparent authority until the prove they have real authority. That proof will make itself evident.

Answer 2

The difference between actual authority and apparent authority would be as in the case of a student and his teacher, and the child's parent or guardian.
The apparent authority or person in charge of that child, while he is in school is his teacher,
but if the child has an accident say, on the playground, and he's bleeding all over and an ambulance must be called, a parent, who is the actual authority, or person in charge of that child must be called. While teachers do have loco parentis rights, which means that we do have the authority to tell the child what to do, when it comes to the hospital, the parent is the actual authority on how the child is to be treated, and must be notified for anything done to that child outside of the school building. Even if the teacher stays with him the whole time.