glucas is exactly correct, but to supplement his answer I have this piece of code I've used myself to make here doc insertion a little smarter.
This advice, coupled with
sh-electric-here-document-mode enabled, make it so that if you type two chevrons the automatic here doc will be created, but then if the next character you type is another chevron, it will revert and you will be left with just <<<.
(defadvice sh--maybe-here-document (around be-smart-about-it activate)
"Do normal here doc auto insert, but if you type another chevron, revert and leave just <<<."
(if (and (= (current-column) 1)
(progn (delete-region (search-backward "EOF") (search-forward "EOF" nil t 2))
Of course this means that if you actually want to start a here doc with a chevron, you'll need to raw insert it, C-q<. So it depends on what you do more of, if you do more here strings than here docs, this can be nice to have, even if you don't, it's rare that you'll want to start a here doc with a chevron and be inconvenienced.