Is there really much difference between these two words? I'm thinking there's not. I won't bore you with the definitions, but when I looked them up (in a dictionary, of all things) they were used to define each other. Therefore, it doesn't do us much good to try to separate them too much because they are very much alike.
Then why bring it up in the first place? I'm glad you asked. There is certainly a fine difference in how I see the concept of these two things, even though there are so many similarities. For example, you easily think of someone "grasping at power", or being "power-hungry". You usually don't think of someone "grasping at authority" or being "authority-hungry." The subtle difference, in my opinion, is that power is something that one person has over other people, where authority is more of a responsibility given to a person. The person in authority still has to answer to whomever has given them the responsibility.
Authority is more like something given, and power is more like something taken. I don't want to make too much of an artificial difference between the two, because they are very similar, but there you have it as I see it.
The reason that I was thinking of this was that a priest brought it up in his homily today. The gospel was about Peter receiving the keys. Something clicked as he talked. So many people have a problem with the pope because of the power that he has. They resent one man having that much power over all the people in the Catholic Church. As for me, I love the pope. I love having that authority to rely on, an authority that was given by Christ. I know that many popes have abused their power/authority, but I don't spend too much time worrying about them because they will have to answer to the One that entrusted that authority and power to them. However, my primary experience with popes has been with those popes that are truly aware and deeply humbled by the huge responsibility in the authority that they have been given. They know that they do not answer to themselves. Ultimately the authority of the pope comes back to Christ, and even Christ answers to the Father that sent Him.
This concludes my impromptu pope post of the day. In honor of St. John Vianney, the saint of the day and the patron saint of priests, don't forget to pray for all priests!