The difference here is that Discourse is not a web app you would just put into a directory, start Apache, and that’s it. Instead it provides its own full stack and as such requires multiple applications being run (PostgreSQL, Redis, Nginx, etc.). This ensures that the user and admin experience is a breeze, using modern web technologies.
The supported way of running Discourse is inside a Docker container, and that requires you to have full root access to your host.
Look at the various hosting offers e.g. from Digital Ocean. They are not too expensive, and you can try things out first. Or you’ll go with a hosted Discourse offer if you don’t want to run a server yourself.