to go away from a place: to leave where one is and move off, often toward somewhere else
This is the ordinary word for leaving a spot and heading off. It pairs the simple idea of going with a sense of moving away from where you were, so it is used constantly in the Gospels for people who get up and leave: a crowd disperses, a healed man goes home, Jesus withdraws to pray. The same word carries equally well whether the writer is looking back at the place left behind (just departing) or ahead to where the person is headed (setting out to do something).
Because its core idea is simply moving off, it stretches naturally in two directions. In one fixed phrase it means to go off after someone, that is, to attach yourself to them or desert what you had, the way crowds went off after Jesus or men go off after forbidden things. And it can describe not just people but conditions and things that are simply gone: a disease leaves a body, the old order of the world passes away. In every case the picture is the same, something is here and then it moves off and is no longer present.
The choice of which English word fits, leave, depart, go, set out, pass away, follow after, is a matter of what is moving and where the writer is looking, not of different roots. Underneath them all is one plain idea of going away.