How was the korean war a proxy war?

The Korean War was the first battle of the Cold War, and first major proxy war fought between the United States and a Soviet communist supported enemy. A proxy war occurs when one or more opposing powers instigates a war and then uses third parties to fight on their behalf.

When the u.s was in the cold war with russia (which wasnt a heated war thats why its called cold) The u.s fought against north korea china and the soviet union. They were allied with south korea a democratic country america didint want communism because they thought it was bad so the helped south korea . the korean war was a proxy war because the u.s didnt actually declare war on russia  but was helping one of its allies