Numerous reasons.
They’re separated from each other by quite a long distance, especially when you consider how much English can vary inside each country and at times within cities in those countries.
Spelling reforms. There was a popular dictionary in the 19th Century in the US which changed the spelling of many words.
Culture. Each culture introduces their own words for things. This can range from words considered proper all the way down to slang.
Influences from other languages. English overall has a lot of words from other languages, known as loanwords, and this has happened differently in both countries.
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