I know you can use NodeJS to fetch different HTML pages depending on the URL. The only difference I can think about is that when using MEAN you can use a database, but with just NodeJS you 'can't', are there more differences?
MEAN comes with MongoDB, Express, AngularJS and NodeJS and it is a easier way to install theses applications. If your application doesn't require MongoDB, Express and AngularJS, I will recommend installing NodeJS and other required applications manually.
The MEAN stack, just like LAMP (Linux, Apache, MySQL, and PHP), is simply a stack of different programs: MongoDB, Express, AngularJS, and Node.js. It's more of a guideline—you can definitely use a different database system such as Postgresql, a different webserver in place of Express such as hapi.js, or a different front-end framework such as Ember.js.
The MEAN one-click is basically an Ubuntu Droplet with MongoDB and Node.js preinstalled and a sample MEAN project placed in /opt/mean, which means that you can manually install these components on a fresh Ubuntu Droplet yourself and get the exact same result.
The one-click is intended to be an image that people can use as a quick start for MEAN projects on which they can build on top.