Websites are client-side-only code - you don’t have access to the project’s server. Websites are great when you’re adding your own content, like text and images, and not trying to communicate with other services via APIs (application programming interfaces, which are like a collection of functions that service provides to talk to it).
When you want to use APIs of other services (like Facebook Messenger, in your case), you’d need to make those requests on your site’s server - so then you’d start with a Node App (or you can remix their Node App from their docs, https://glitch.com/edit/#!/messenger-platform-quick-start).
So, Node Apps are like Websites but you have access to more of the “guts” of the project’s container, and the ability to import modules from npm and run scripts for building and testing your app. But also sometimes Node Apps (like in the case of that messenger starter app), don’t have a site for users to see - https://messenger-platform-quick-start.glitch.me/, for example, shows a “Cannot GET /” error because the project only has server side code. The app works, but it’s not a website for people to look at, it’s a bot for Facebook Messenger.