... and Chrome OS also provides a terminal emulator to go with its shell.
and that makes terminal emulator the same thing as shell?
The confusion here is that presumably "SSH" is not something "provided" by the shell, but merely something that you can run with the shell.
I'm not actually sure that's true. It's not a full-fledged ssh client; it may well be a shell builtin. (It can't be the standard openssh client, because that lets you escape to a real shell.)