Emacs has Tramp, so you can open and edit the remote file right on your computer and emacs takes care of shelling into the server in the background and applying your edits.
Tramp also works with things like dired (Emacs directory/file browser) and GDB. Which means that nowadays, I often don't even need to explicitly open a shell on the server (and if I do, it's M-x shell). Tramp also handles tunneling connections and user/privilege switch. So, for instance, I can open my remote home directory, as root, on some server in another network like this:
C-x f ssh:me@public-server|ssh:me@private-server|sudo:private-server:/home/me
And it will just work, opening a dired view of the home directory on remote server, with root privileges. Further commands (e.g. opening files) will also work on the remote, mostly seamlessly.
Internally, Emacs manages shell connections and translates your operations to shell commands; e.g. opening a file will copy it over to your system, and saving it will copy the altered version back.
C-x f ssh:me@public-server|ssh:me@private-server|sudo:private-server:/home/me
And it will just work, opening a dired view of the home directory on remote server, with root privileges. Further commands (e.g. opening files) will also work on the remote, mostly seamlessly.
Internally, Emacs manages shell connections and translates your operations to shell commands; e.g. opening a file will copy it over to your system, and saving it will copy the altered version back.