differences in dictionary spellings, mostly webster's used "-or" at the end of words, johnson's used "-our" (honor, honour) metathesis got codified in american english but not british english, thus "-er" instead of "-re" (saber, sabre) sometimes from orthographical simplification in american english, such as logue > log (catalog, analog) or æ and œ > e so really all sorts of reasons
see, the source of -or/-our words are mostly from latin, right when they were originally borrowed from latin, the ending was spelled -or. when the normans invaded england, they brought the -our ending that old french had for them with them. that ending was applied to old borrowings as well. so really you can blame the original problem on the french. after the british stopped aping the french they reborrowed more terms from latin, but there was confusion as to whether those words should be spelled with -or or -our: the general consensus was for -or, but still not a decided thing. webster's just used -or for everything on the basis of that being the original spelling. johnson's used -our in the french-gotten cases.
Do you think there was a strong cultural motivation to try to distinguish or establish America independently from England or more of a natural process?
no i don't think that at all - this sort of thing happens naturally. i don't think anybody in the united states aimed to make their spellings different than the british.
What's the most fascinating thing you know about language or linguistics?
that's a hard question to answer because i find it all really fascinating. i don't think i could call anything "the most fascinating". i really recommend anybody reading to learn more about linguistics. i wouldn't call it useful knowledge all the time, but i think it's all interesting knowledge.