(I picked "\C-m" out of all possible spellings because AFAICT it's the
one that comes up most often in the Emacs source tree, but maybe it's
not the best possible one.)

Thank you for your time.


References:

- (emacs) Keymaps

> Most modern  keyboards have function  keys as well  as character
> keys.  Function  keys send input  events just as  character keys
> do, and keymaps can have bindings for them.
>
> …
>
> On  text terminals,  typing a  function key  actually sends  the
> computer a  sequence of characters;  the precise details  of the
> sequence depends on the function key and on the terminal type.

- (emacs) Named ASCII Chars

> Emacs can distinguish  these two kinds of input  if the keyboard
> does.  It treats the special  keys as function keys named ‘tab’,
> ‘return’,  ‘backspace’,  ‘linefeed’,   ‘escape’,  and  ‘delete’.
> These   function   keys   translate   automatically   into   the
> corresponding  ASCII characters  _if_ they  have no  bindings of
> their own.
>
> If you  do not want  to distinguish between (for  example) <TAB>
> and  ‘C-i’,  make just  one  binding,  for the  ASCII  character
> <TAB> (octal code 011).  If you do want to distinguish, make one
> binding for this  ASCII character, and another  for the function
> key ‘tab’.
>
> With an ordinary ASCII terminal,  there is no way to distinguish
> between <TAB>  and ‘C-i’  (and likewise  for other  such pairs),
> because the terminal sends the same character in both cases.

- a *scratch* buffer:

> (kbd "RET")         ; "^M"
> (kbd "\r")          ; "^M"
> (kbd "C-m")         ; "^M"
> (kbd "<return>")    ; [return]

- on X:

> C-h c ⏎ ; RET (translated from <return>) runs the command newline

- on a TTY:

> C-h c ⏎ ; RET runs the command newline


In GNU Emacs 27.0.50 (build 4, x86_64-pc-linux-gnu, GTK+ Version 3.24.12, cairo version 1.16.0)
 of 2019-12-09 built on my-little-tumbleweed
Repository revision: 51176ee81e8e773d8b6ac06dd153846abee0c0f4
Repository branch: master
Windowing system distributor 'The X.Org Foundation', version 11.0.12006000
System Description: openSUSE Tumbleweed

Configured using:
 'configure --with-xwidgets --with-cairo'

Configured features:
XPM JPEG TIFF GIF PNG RSVG CAIRO SOUND GPM DBUS GSETTINGS GLIB NOTIFY
INOTIFY ACL LIBSELINUX GNUTLS LIBXML2 FREETYPE HARFBUZZ M17N_FLT LIBOTF
ZLIB TOOLKIT_SCROLL_BARS GTK3 X11 XDBE XIM MODULES THREADS XWIDGETS JSON
PDUMPER LCMS2 GMP

Important settings:
  value of $LC_CTYPE: en_US.UTF-8
  value of $LANG: en_US.UTF-8
  value of $XMODIFIERS: @im=local
  locale-coding-system: utf-8-unix