What is the difference between an Oscar and an Academy Award?

No, and Academy Award is not exactly the same thing as an Oscar (but almost). An Academy Award is an award presented by the Academy of Motion Picture Arts and Sciences. The Academy presents about seven different types of awards. The most popular award that they present is officially known as the Academy Award of Merit (Best Actor, Best Actress, Best Picture, etc). The prize for winning this award is the Oscar statuette, so most people refer to the award as the Oscar. Some of the other award winners also receive the Oscar statuette, and some of the other award winners receive plaques or scrolls. One of the awards is always a bust instead of the Oscar statuette. A couple of times the Oscar statuette has been modified for special awards. Shirley Temple received a pint sized Oscar statuette when she was presented with a Special Juvenile Award. And Walt Disney received an Oscar statuette with eight tiny Oscar statuettes when he was presented with a Special Award for the creation of Snow White and the Seven Dwarfs - the first animated feature.

Yes

basically the 'oscars' is just a nickname for the academy awards