In intransitive terms the difference between tumble and slip
is that
tumble is to fall end over end while
slip is to move quickly and often secretively; to depart, withdraw, enter, appear, intrude, or escape as if by sliding.
In transitive terms the difference between tumble and slip
is that
tumble is to smooth and polish a rough surface on relatively small parts while
slip is to cause to move smoothly and quickly; to slide; to convey gently or secretly.