But do you approach the actors any differently? (or is it the same as with film)
You stand and walk toward them, confidently and without sudden moves, lest they get spooked.
But seriously, the answer is yes and no. How about that for clarity? Acting for the stage and acting for film are the same, philosophically, but different, technically.
Philosophically, an actor on stage or film embodies a character in accordance with his or her own training and technique. It is NEVER the responsibility of a director to interfere in this process (unless you are an acting teacher from whom the actor has solicited such training). It IS the responsibility of the director to cast the right actor for the role in the first place, whether for stage or film.
Technically, an actor's stage performance is MUCH broader than a performance for camera. On stage, the actor must broadcast his or her dialogue to the back row of the auditorium, and gestures must be large enough to register with the audience. If working with amateurs, a director is occasionally obliged to remind them of this, but experienced actors will do it automatically.
In addition, because the play is performed in a single, uninterrupted "take" (except for an intermission break), the director must manage the tempo of the performance. In film, this is done by the editor in post. Also, a stage director must keep in mind the composition of the stage at any given moment, just as a cinematographer would, in order to properly communicate the story. This is chiefly accomplished by the placement of the actors in the space.
In order to direct well in either medium, you'd better know your shit going in, or the actors will not want to work with you again.