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There are basically two main types of website - static and dynamic. A static site is one that is usually written in plain HTML and what is in the code of the page is what is displayed to the user. A dynamic site is one that is written using a server-side scripting language such as PHP, ASP, JSP, or Coldfusion.
A static website doesn't change. It's usually just a bunch of html, css, and possibly javascript files that are served by a simple webserver.
A dynamic website has a backend written in a language like PHP, Python, Ruby, Node.js, etc. These sites can take user input and change their content based on databases, external APIs, etc.