I'm writing a fictional story that has two separate, parallel worlds - I wish to distinguish both worlds by referring to them as the 'first world' and 'second world'. The first world would be Earth as we know it and the second as my fictional world. My query is, would titling them as the first and second world be too close to the out-dated model of the ranking scheme used to describe the state of countries from the poorest to the wealthiest? I don't want to carry any political or ideological connotations if I were to use these terms of distinguishing both worlds in my story.
I don't think so. There are other fantasy and fictional stories that use the same descriptions. You could, if you wanted, change it up just a little like with Stephen King's "All-World" and "Keystone Earth".
Who, in-universe, has titled these worlds? If it's, say, kids, then names like 'home' or 'the real world' and 'the other place' or something like that would make sense. If it's scientists, then you might want something like Earth Alpha and Earth Beta. First world / second world might carry some baggage, but might be totally fine, too.
I don't think referring to places as First World... Third World... is outdated at all when it come to the state and living conditions in countries. And as soon as I read your first paragraph that is exactly what I thought of. I think even World 1 and World 2 would be better than First World and Second World.
I don't think that the issue is political or ideological connotations so much as just plain confusion. I would use some other term. (Edited to add: Though I do find myself imagining a "who's on first" style dialogue.)
Which one is first and second? Why are they organized like dates? What's the most noticeable difference of the two worlds? Does the other world have an orange sky? Okay so it's Orange World and Blue World. How official even is the naming? You could even have characters refer to the other worlds as other names. The Otherworld, that place with the tall buildings, maybe name it after slang from the other world. You can be way, way more playful with this than just numbers.
Yes, I think it would carry that connotation. But my bigger concern is credibility. What do the characters who live there call their world? Could be 'Secondus' or 'Junior', if they know it's an offspring of the original "Earth" or world. Then you could call it whatever the residents call it. If they don't know; if they think of their world as simply "Earth" or the world, then you do need another designation, like Alter-world or something. I can't think of a variant of Fringe's "Walternate" just at the the moment, but you might want to play around with similar words that are relevant to your story.
