The Cold War was a long time ago when the United States and the Soviet Union (now Russia) were both very powerful countries, but disagreed with each other. They fought each other all around the world, without ever going to war with each other. This was called the Cold War because no side ever wanted to start a real fight.
Cold War II is similar to Cold War, because it is also a time of tension between the United States and Russia. They are not fighting each other in the same way as during the Cold War; rather, they compete with each other in other ways. They fight using words instead of guns. Each country is trying to gain influence in other countries, and each is trying to prove it is stronger than the other. In some cases, they get so angry at each other that they do things to try and hurt the other, like when they punish each other with economic sanctions.