"Tee box" is an informal term, a colloquialism; "teeing ground" is a term used in the rules.
In the Official Rules of Golf:
"The 'teeing ground' is the starting place for the hole to be played. It is a rectangular area two club-lengths in depth, the front and the sides of which are defined by the outside limits of two tee-markers. A ball is outside the teeing ground when all of it lies outside the teeing ground."