If I have just
(set-face-foreground 'font-lock-comment-face "red")
(set-face-foreground 'font-lock-string-face "green")
in my .emacs, emacs uses the same font-lock for Python strings and for Python docstrings.

What should I add to my .emacs so that comments, strings, and docstrings are distinguished?
This answer suggests that it is possible to do so.
Built-in python.el provides
font-lock-doc-facevia python-font-lock-syntactic-face-function.python-mode.el uses
font-lock-doc-face, givenpy-use-font-lock-doc-face-pist. You can customize that variable.