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Client-Side Web Development
Client-Side Web development consists of anything that is run, or displayed on the end users machine. It includes anything the user sees or interacts with on a web page, examples of this could be HTML, CSS, or JavaScript.
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Server-Side Web Development
Server-Side Web Development is everything that runs on the backend of a website, this includes scripts that run on a seperate machine from the client and returns a custom response based on the users request. This could include databases like MySQL, or things like PHP that render a custom page server side and sends it to the user.