All languages change over time. You can even see this in modern English, with the introduction of new terms and using old words in new ways. Generally, a community of people is going to have their language drift in the same way, but what happens when the community splits?
Barring an outside force that standardises language, the two different communities are going to have their original language drift in different ways. As time goes on, this is going to manifest as different–but related–languages. You can see this with many of the Romance languages, all with common roots in Latin, but have since drifted apart.
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