1. How were each of the theaters of WWII different?

2. How were they similar?

The three theaters were the Pacific, the European, and the North African.

The role of the US in each one was to fight on the side of the Allies. They were able to launch large offensives against mainland Europe, one staged from Britain (the D-Day Invasion), and the other partially from North Africa (Anzio, in Italy).

In the Pacific, it was a bit more difficult--they had to fight the Japanese for every single tiny little island, and the fighting was the difficult, hand to hand type quite a large part of the time. When Japan signed the unconditional surrender after the US dropped the two nuclear weapons on them, the US was planning to gear up for an invasion of the islands of Japan. It was estimated that that invasion would be the most difficult and deadly of the war.

Of the three theaters, the US was least involved in North Africa, but even there, we played a good-sized role.

I've gotten you started, now you know what to look for and you can go research on your own.