I keep forgetting the current fashionable way of accessing a machine remotely with a graphical terminal.
Also which client is popular right this second. To answer that, I should note for myself that a popular swiss army knife client for Linux is Remmina.
In practice this might not always be sufficient since it needs an X server on the client machine and supporting SSH server config plus an X app on the server machine. In principle this should be a fast way of doing things but it seems unresponsive to me and the integration between remote and local machines can be unintuitive. Still, if you have to plug two machines together and they both run X (e.g. because they are both linux machines) this is smooth.
My last two campuses liked the protocol Nomachine NX which I confuse with X2Go.
As far as preferred clients, my campus, UNSW, supports x2go which has a qt client and some python thing called pyhoca. The web presence for this protocol looks worryingly amateur. But it does seem to be less laggy over bad internet connections when you set it up right.
VNC is AFAICT not cool any more but was what we used for a while there. It uses some protocol called RFB. I think this si the one that Apple favours? It can also be tunneled over SSH, but it not the same thing as X11 forwarding, specifically because it does not actually need X11 to be run on the client or the server; any old screen display will work, because this just shunts pixels from the server to the client, rather than specific windows and interfaces and whatnot. The main barrier for use is that last time I looked into using this there were so many different implementations and options with various incompatibilities and speed and quirks that my brain shut down and I decided to world from the command line instead. Anyway, the original RealVNC software is blessed by Raspberry Pi so maybe that will be a good default option for next time.
Remote Desktop Protocol Microsoft’s one. There is some patent issue.
This popular display protocol for virtual machines is also availabe for remote desktops. I suspect this is even nerdier than usual.