Yes, Discourse is pretty different. It runs on Ruby on Rails and not on PHP.
You cannot just upload the files to a shared hosting environment. You have to get a Virtual Private Server (VPS) and use Docker. You could also get specialized Discourse hosting if you are not familiar with that.
In order to migrate your current forum: there is a script available to convert phpBB to Discourse, but this is something you could also ask for in marketplace.