I'm going to throw a wild card and have the electric country a modern civilisation (but not like us). Otherwise, the electronic society would also be using coal or something similar (like oil, gas, uranium, etc.) :P.
I'm also making the electric nation a brand new nation instead of just plopping America or the UK etc. into this scenario because they are just too OP with their nukes, faster than sound planes and near indestructible tanks.
So the electric country is the world's current superpower, they are the richest, has the most military power and endured many great wars without much loss. (kind of like America right now) They made electricity so efficient that they stopped using coal altogether because coal is too inefficient, costly and pollutes the world which most of the people wouldn't be so happy about it.
They built their first satellites and found a new continent that has a lot of concentrated Co2, so they decided to investigate and found a somewhat advanced society (at least in that continent) that ultimately was driven by coal. They immediately seized the opportunity and decided to trade with them, while the steam country, being ripped off by the electric nation. The steam nation starts to become well aware of the electricity nation and its powers, so they decided to make a modernisation revolution but realising that they can't keep up with the rapidly increasing technology of the electric country. They decided to steal from the electric country instead which at first the country was all right with, but they started to take expensive, secret technology, so they demanded the steam nation stop. However, they didn't so the electric country declared war on the steam country.
The steam country just got the technology, however, so they didn't have the time to implement most of them into their military, so they relied on mixing the armies together (mostly steam technology with some stolen ones, so it stays mostly a steam country without being kerb stomped by the electric one)
So that's my idea hoped you liked it. I tried to make it as world war like as possible (like how it was so easy for them to start wars and stuff) without it becoming a cultural conflict, but it still might have some lingering in there ^-^