The Cold War was different from other wars in the sense that it wasn’t a physical war, rather more of a logical and timely war.
In the Cold War, no weapons were used; no damage was done between the two opposing forces. The United States and the Soviet Union (contemporary Russia) were in competition to hone their skills in achieving titles of things such as “first person on the moon,” “first space shuttle to revolve around Earth,” and “first animal on the moon.” Because the Cold War was more of an achievement competition than war meant to hurt each other, it wasn’t necessarily a war. That’s what made it different from other wars.