Is the Soviet Union the same as Russia?

No, it isn't. At the time the Soviet Union was still in existence, "Russia" was one part of the Soviet Union, although by far the largest and most dominant. In December 1922, Russia, then known as the Russian Soviet Federative Socialist Republic, joined with Ukraine, Belorussia and the Transcaucasus Federation to form the Soviet Union. After that over time, the Soviet Union annexed or took under its control many other nearby republics, such as Uzbekistan, Khazakstan and others.