In intransitive terms the difference between tumble and stagger
is that
tumble is to fall end over end while
stagger is to begin to doubt and waver in purposes; to become less confident or determined; to hesitate.
In transitive terms the difference between tumble and stagger
is that
tumble is to smooth and polish a rough surface on relatively small parts while
stagger is multiple groups doing the same thing in a uniform fashion, but starting at different, evenly-spaced, times or places (attested from 1856).