Answering what caused the split is what I want to do here, and that's why I'm commenting, but first I think I probably need to get into the origins of these words a little bit.

"Coke" is just a case of metonymy where a specific brand of an item becomes the go-to word for all of that item even if made by another brand. It's the same thing behind a lot of Americans calling facial tissues "Kleenex" or your mom calling your XBox a Ninendo.

"Soda" is a shortened form of "soda water" which referred to a carbonated mineral water, the "soda" part representing the mineral sodium bicarbonate.

"Pop" is a reference to the sound of the cork coming out of the bottle.

Quoting here from the Online Etymology Dictionary, because it sums it up well enough that I don't think it needs re-writing:

The meaning [of 'soda' as] "carbonated water" is first recorded 1834, a shortening of soda water (1802) "water into which carbonic acid has been forced under pressure." "It rarely contains soda in any form; but the name originally applied when sodium carbonate was contained in it has been retained" [Century Dictionary, 1902]. Since 19c. typically flavored and sweetened with syrups. First record of soda pop is from 1863, and the most frequent modern use of the word is as a shortening of this or other terms for "flavored, sweetened soda water.

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Ok so now to the actual question: What caused the split.

What happens in these cases where you find very strong correlations to regions and vocabulary is that there's a certain cultural influence at play. You see a clear split between the South and the rest of the country, with the south using "coke", and then if you look as "soda" vs "pop" in areas where there's a clear distinction, what you see is that areas in the St. Louis area are saying "pop" running up along the I-55 corridor almost all the way to Chicago, as well as the coast of Wisconsin and then California and New England. Each of these areas are essentially cultural regions.

You may have heard the term "shibboleth"or maybe not. In case you haven't, a shibboleth is a word or phrase that, based on how someone says it, the other people around immediately are able to identify whether they are from that area or not. This exists in a great many languages. Often it's neutral; they're just from somewhere else. But historically this has also been used to specifically target or marginalise outsiders.

So by "cultural regions" above, what I mean is that in these areas there are certain things tying their language use together, and where the sort of community cohesion that supports things like shibboleths can occur. One major factor behind this cohesion on the scales you see here has to do with things like broadcast media, as well as simple social influence. On the media side of things, historically you'd have local broadcast areas based on these urban centres for things like radio and television, and through this one term or another would catch on and spread until it eliminated the others. If you grow up and the media is calling it soda, that's the word you're going to be learning for it.

For more general social influence, people tend to move around within a city or region or interact with others from that city or region more so than with people from far away, and for those coming from elsewhere, there's significant pressure to accommodate to the local vocabulary. You can see some of these urban centres quite clearly on the map, even beyond just St Louis and Milwaukee. Indianapolis, for example, is a clear red spot in Indiana. Why Indianapolis has this tendency toward "Coke" I couldn't say, but that's clearly what's happening in the urban area and the surrounding counties which are getting their local media from the city.

State lines also come up in some cases; You can make out Oklahoma as being distinct from Texas to the south in about half the counties for which there is data.

The point is that very little of the clusters and shapes you're seeing are random. There are a couple odd spots, like the bright green area in New Mexico which is basically a state forest and surely doesn't have many people to have been asked how they refer to a soft drink, but generally these follow along cultural regions and patterns of human movement and the corresponding cultural influence. Of course while regions/cities/neigbourhoods/countries are not uniform in how they use language, they do have a significant impact in the overall picture of language diversity. You will find exceptions, which is why there's a lot of in-between colours on your map, but the trends are still pretty apparent.

Hope that helps. Let me know if anything I wrote was unclear.