Not sure about this (I haven't used either, just looked at their sites), but I believe those are terminal emulators. They're the thing that displays the shell and handle input and copy/paste etc.

The shell is what actually handles key presses and produces the output (handling commands, input/output redirection, etc).

They're not the same thing - I bet you could use fish inside cmder or iterm.

I'd say it doesn't since neither of those are shells. They're both terminal emulators that run a shell within them, usually bash for linux/mac or cmd for windows.