Actual authority is the power given to someone to do a thing or carry out an assignment. it specifies which duty to do.

ostensible authority is power derived from the power given to do an act. This authority is derived as a result of the actual authority given to do an act.

Ostensible is an adjective to describe something as seeming, apparent, or appearing to be true, but not necessarily so. Example sentence:

People sometimes believe media statements because of their ostensible authority.

apparent -apax

"The ostensible reason for the meeting turned out to be a trick to get him to the surprise party."

My father was ostensible to go to the Railway Station to pick up my grandfather.