That's the original definition. I think now first, second, third are used to annotate which level of development a country is at. Especially that now, not all developing countries are equal.
It's more nuanced than that. First was the USA, the first nuclear state (and the west / allies). Then the Soviets. The Third World was the anticipated rise of the nations that would join us on the world stage, a hopeful and optimistic term[0]. Then we deliberately sabotaged them and kept them under our boot to extract resources.
Third World is now a slight for developing nations.