Ok, first things first 
Your NAS is only accessible to people who are logged into your network. So anyone who has logged into your network (has a valid username and password accepted by your router) can see the NAS, and is able to access any public share folders on it (and also the private shares if they provide appropriate log-in credentials for the NAS itself).
Basically your NAS is just another computer on your network, but one without a screen or keyboard. It runs Linux, and its whole purpose is to just share the drives attached to it with other computers also on the network, plus to provide a small self-contained webserver to support its configuration dashboard.
The dummy/live demo you’re remembering is accessible from the WD apps for tablets and phones. If you install the app on an iPad or an Android device and connect it to the internet you will be able to see the demo (and if you’ve enabled cloud access on your NAS and set up access for your user(s) via their email addresses then they can remote access your NAS as well). Personally I don’t use the apps, so I can’t comment too much there (although I did play with them right at the start of my ownership of my NAS, I’m going from memory here).
Dashboard remote access is possible (there’s a setting in the dashboard for it), but again I’ve never tried it as it sounds like a security risk to me. If I need to do something like that, I make a remote connection to a machine on my network (normally I use Google Remote Desktop) and then just open Chrome remotely on that machine and connect to the dashboard normally within my network.
