Warfare refers to the general act and art of waging war. It does not refer to a particular war. We use the term "biological warfare" to refer to the use of biological toxins as a weapon of war.
War is sometimes used in the same way of "warfare", but is more often used to refer to a particular armed conflict.
You would refer to the "Second World War" or the "Great Patriotic War", but never the "Second World Warfare".