I'm not 100% certain if this will help clear things up for you but I'll try to break down each application/protocol you mentioned. Not sure what you mean by 'RAT'.
Consoling into a system is generally paired with telnet/SSH.(layer 7 of the OSI model.) You're viewing the 'terminal' or 'console' of a system and aren't able to view a virtual desktop with telnet/ssh. You would telnet or SSH into a system if you only wanted to run console based commands. System maintenance(configuring) or scripting purposes(setting up custom scripts) are best done in the console generally.
When going into a system to view the desktop virtually, you're "remoting in" rather than "consoling in." This would be done via RDP or another virtual application like teamviewer. RDP etc. is also a Layer 7 application/service of the OSI model. People use the virtual desktop to operate applications that can only be troubleshooted or operated via the GUI. For instance browsing the web is best done through a desktop GUI (aka RDP, teamviewer, or the physical desktop). You wouldn't want to browse the web via the console(there are text based browsers you can use via a console but it's horrible to browse the web with them.)
VPN - Virtual Private Networks, they're meant to be used to interconnect networks that otherwise would not be connected. AKA allowing outside networks access to inside private networks via tunneling from what's generally a public IP entry point from the web to your local private network, hence creating a Virtual Private Network. They run at the layer 2/3(data/network layers) of the OSI model.
There's many types of VPN's, PPTP, IPSEC etc. They're generally used with encryption(not sure what IT tech would not enable encryption on them) and what they do is encapsulate the data you're wanting to transmit and only the other party that has the access key can decrypt the tunnel packets.
These are all tools and are to be used when they'll make life easier. There's multiple ways you can always do things but its best to choose the option that suites the task.
Hope this helps clarify them.