In our dojo, tenkai is used for a turn on the spot where you don't step just turn on the balls of the feet, like in one of the descriptions above. (To be completely accurate usually there's a small step with the front foot first to free that foot and to have some irimi in the movement). You could also say it's the same as the beginning of tenkan before one foot takes a step back, that's actually how we teach beginners.
But that's just us, anybody else better ask their own teachers.
kvaak
Pauliina