Set out is a phrase which has varied meanings when used in different contexts.

To set out means to begin a journey
They set out for home quite early this morning.

set out also means to begin an undertaking or an attempt
He has set out to prove his innocence.

set out also means to design or plan
He has set out the complete pattern of events on this show.

Set off is basically used to mean to start or ignite a series of events;
His report set off a series of discussions and meetings among the administrators.
However, the phrase is also used to mean to start a journey, just as set out
They set off/out for Mumbai.