Power and authority may seem the same in the beginning but actually, they are different. Power means that the person can influence other people and also control their actions. Those who are in authority usually have the power but usually, those who have power do not need to have positions to influence other people.
Those who are considered as authorities may have been elected into the office while those who have power may have the ability to make people move according to their will because of their skills and knowledge. There are instances when power and authority may go hand in hand but there are also moments when someone in authority will not have the power to make people follow.