As far as the European theater goes this is correct. Russia’s part was vastly larger than ours.
One of the most important battles of WWII is one few even know about. The Battle of Khalkin Gol in 1939. It’s where Zhukov made his bones. And it happened despite the fact that Japan and the Soviet Union at the time were not technically at war with each other.
But the defeat of the Japs there, greatly changed the course of the war, mainly that Japan and the Soviet Union, wound up signing a non-aggression pact, which meant that Japan would not help Hitler against the Soviet Union.
The Soviet Union only declared war on Japan at the end, so they could get the spoils of half of the Korean Peninsula, and the Salkhalin Islands. And frankly, if not for Fat Man and Little Boy, they probably would have gotten at least half of Japan, as well.