Second world doesn't mean axis powers, it represented the Soviet Union and Soviet aligned countries.

Its a cold war term. The terms represent the two remaining superpowers after WW2.

1st world = The US and US aligned countries

2nd world = Soviet Union and Soviet aligned countries

3rd world = Non-aligned countries. Which just happened to be mostly under developed countries, which is why the term is now used for that. It didn't actually mean under developed at first. For example, Switzerland is technically a 3rd world country despite being rich and highly developed.