The more acurate (and somewhat more PC) term for what is commonly known as the Korean War. The idea of 'conflict' versus 'war' is because one of the primary parties, the Unites States, did not actually declare war on North Korea, instead sending troops as a 'police action' in the same way that was seen later in Vietnam.
AwkwardSaw says "You may want to mention ... that while the US never declared war on Korea, it was the first war in which the United Nations did."