Set off is used when it is a cause to happen, a cause to explode or a cause of a sudden reaction. Eg. If the soldiers' bonuses are not paid, it will set off a march on the nation's capital. Set out refers to the beginning of an undertaking, to a display or the start of a journey.

When you set out, it means you're determined to do something or you're going on an adventure. Example: "He set out for the day with a backpack full of supplies" "When I set out to do something, I finish it" Set off means to make something explode. It's typically said of an angry person or fireworks.

'Set off to' is commonly used to indicate the beginning of a journey or trip, while 'set out to' is used to express the intention or purpose of an action or goal. Therefore, the choice between the two depends on whether you are referring to physically starting a journey or embarking on a specific task or objective.

Set off is just to go somewhere. Set out can be either to go somewhere, or to achieve something. It implies something more difficult that just 'set off' would seem. It sounds like going on a mission.