Using the terms that you have provided here, the western democracies' response to totalitarians was one of appeasement in the first time period that you mentioned and one of confrontation in the second time period.
In the first time period, the western democracies did not want to confront totalitarian states like Nazi Germany. They felt they were not ready for war and hoped that appeasement would prevent Germany from expanding too far.
During the Cold War that followed WWII, the western democracies were much more confrontational. They tried to contain communism by opposing it aggressively whenever it seemed to be expanding. This was very different than their actions towards Hitler had been.
After WWI, the European democracies were unable to check the power of the rising totalitarian states. Early on (early 30's), the European nations had depended on the promise of the League of Nations to maintain peace and to rogue nations in line. The League of Nations was weak, unable to enforce its own resolutions and, therefore, unable to live up to its promise.
WWI had been devastating to Great Briain & France both in the physical destruction of the infastructure and psychologically as these nations feared a repeat of the bloodbath that had been WWI. European leaders quickly adopted a policy of appeasement toward Nazi Germany. As Hitler made moves into the Rhineland, Austria, the Sudetenland, etc., he claimed to only want to peacefully reunite all ethnic Germans under one flag. Despite knowing that Hitler had remilitarized Germany, Great Britain and France were quick to take him at his word out of a fear of forcing his hand and starting another war. Their goal was to avoid another war at any cost.
For its part, the United States had quickly reverted back to a foreign policy of isolationism despite emerging from WWI as the only nation strong enough to check the power of the European dictators. Basically believing that what happened in Europe was Europe's problem. During the 19th century, this policy had served America well. However, as a result of the Industrial Revolution and a growing commerical connectedness between nations this policy of isolationism would fail miserably. Very few recognized that what was happening in Europe (and also the Pacific) would eventually involve the United States whether we liked it or not.
After WWII, the United States recognized that it was this policy of isolationism that had allowed Hitler and the Fascist dictators of Europe to rise to power unchecked. During the Cold War that followed, the United States adopted a more proactive foreign policy and was williing to more aggressively challenge the rise & spread of communist dictators throughout the world. The goal was to do what was necessary to limit the spread of communism short of going to war. The U.S. did fight two smaller wars by proxy (Korea & Vietnam) but never directly challenged the Soviet Union. Hence, the Cold War. The period from 1945 - 1980 was more a war of indirect confrontation and attrition. Neither the United States nor the Soviet Union had a burning desire to start a hot war that could quickly turn nuclear.
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