The C-c C-s binding mirrors the export and writable export bindings.
embark-export is used for type specific exports (such as buffers to an
ibuffer buffer), not for verbatim exports. This is most noticeable if
you want to export a variable list, which gets you to an apropos buffer.
if you just want a list of things to keep around,
embark-collect-snapshot is the tool for the job, but having it be only
on C-; S makes it harder to reach and less visible. C-c C-s is a nice
visible thing to have around.