They are all correct, but they have overtones/a sense of politics. It depends how polite and how accurate you want to describe a country.
In the Cold War, in people's minds the world was categorised into the 'first world' countries, i.e. Western European type countries. Eastern Europe and communist countries were called "2nd world' and all the rest of the world, (i.e. all the African countries, all the south and central American countries, all the Asian countries) were called '3rd world countries'. There were some exceptions to that idea - Japan, South Africal ,etc were not the same as their neighbours.
"Undeveloped" or the more polite "under-developed" could refer to the people and the land too. Australia might be called "under developed' but that is because of climate, infrastructure, etc and not because of education with the people.
Some African countries might be called "undeveloped' because of a lack of infrastructure, roads, electricity, banking system, etc (i.e. mostly because of a lack of money). or it might be called undeveloped because you refer to the education of the people, which create and pay for the infrastructure.
How you call a country and how you describe a people/nation reveals things about your attitude. You could say things politely or bluntly. You can say it is 'bad' or you can say it is 'not as good as it can be'.
If you call a country or people 'backward' , it is a strong and derogatory name. It might be correct, but it is not polite. It infers a lack of technology, education, etc.