I dont think I have ever seen failing former super powers such as Russia, or countries that have developed more advanced economy and industry but are not yet superpowers themselves, referred to as '2nd world countries'. Not on the news, not in my studies, not on the street.
If people are referring to these nations as '2nd world countries', then they are doing so merely out of convenience or because they never understood what '2nd world' meant in the first place.
The term is an archaic one that no longer applies in the modern world, and certainly you shouldnt find anyone teaching students that it can be applied in this way.
CG does make a valid point that terms such as 'Islamic' countries/world or 'Christian' countries/world are becoming more widely used.
This is true, and is due to how we view the world around us. In the 1980's we viewed the world on a technological or military basis. In the 1990's we viewed things along their economic relevence. In the post 9/11 world however the world is often see, described and understood the world along religious/cultural lines.
In 2000 when I completed my studies, the term 'islamic world' was rarely, if ever, used, nor did this world appear often on our TV screens. Now its widespread. It may be another 20 or 30 years before we once more 'reclassify' how we see the world.