There are no relations between the two wars, but some of the major countries (such as the Soviet Union, China, U.S., etc) played important roles in both wars.
The Cold War was pretty much the United States opposing communism, and it greatly relates to the Vietnam War because communists wanted to take over South Vietnam, and since the US had made opposing...
Communism was seen as the greatest threat to the free world. The Vietnam war was "theoretically" an act of military might to discontinue the "domino theory" (spread of communism).