The verb {mej} refers simply to leaving one's current location, while {tlheD} generally implies setting on a journey with a goal or destination in mind.
But that's rather strange, since normal sane people, never leave any location without a goal or destination in mind.
Normal, sane people, don't suddenly get up, leave their house,work,etc without a goal or destination in mind.
Normal, sane people, don't suddenly find themselves in the street, just wandering without a goal or destination in mind.
I can't think of a single instance where {tlheD} isn't the word which actually needs to be used.
~ Dana'an