The difference between these two concepts has to do with right and might. Power can be defined as having might while authority can be defined as having right.
Power is generally defined as the ability to get someone to do something the otherwise would not do. This is the ability to influence what happens in a given situation. A person can derive their power from a number of sources. A person who pulls a gun on me and tells me to give them my money clearly has power and that power derives from the fact that they can kill me. Thus, power can simply be a matter of having might.
But there is one sort of power that can be called authority. This is a kind of power that those who are acted upon actually accept and agree with. If I belong to a church and the church says that I must give 10% of my money as a tithe, I might accept this because I accept the authority of my church. In both bases, money is being taken away from me. But in the second case I am voluntarily giving it up because I agree that the church has the right to take it away from me.
Thus, power is simply the ability to affect the outcome of a given situation whereas authority is the perceived right to affect that outcome.
Power and Authority are two words with separate meanings. The only difference between them is the willingness to follow or forced to follow.
Power is the control over people to make them or force them to follow something they might unlike or unwillingly.
Authority is the ability to influence people to follow willingly.