I heard someone mention a "second world country" just now; didn't that mean the Soviet Bloc, when it existed?

You are on the right track. Traditionally, the "1st world" referred to the industrialized and democratic countries and the "2nd world" referred to industrialized but non-free societies, like the communists, but it didn't mean only communists. There are still industrialized, non-free societies, like China or any of the Arab nations, so the second world still exists but doesn't necessarily refer to communist countries.

The "3rd world" refers to undeveloped and non-democratic countries; and the "4th world" refers to those peoples who still live traditional subsidence lifestyles like some tribes in the Brazilian rain forest, the Inuit peoples of the Artic, and the Aborigines of Australia.