In more technical terms, a centralized system would be like you building a website. You would have a single server or maybe a cluster, but it all works toward the one product, and you're managing everything with that website.
A distributed system is like the internet. No one person owns the internet, anyone is free to add new servers wherever they want. But in order to be a part of it, you need to follow a set of protocols to ensure that your new server plays nicely with all the others already on the internet.
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