Consider the usual definition of second world, the Communist bloc (Soviet Union and the Warsaw Pact nations). Now according to the official definition, Cuba, Red China and North Korea should also be considered Second world, but in usual usage are considered Third World.
The usual definition is done by example. First World is the United States, Canada, Western Europe, Australia, New Zealand and Japan. The Second World was typically listed as Soviet Union and the Warsaw Pact (Poland, East Germany, Czechoslovakia, etc.). The Third World was everybody else, "developing" nations.