The area of the theatre in which the performance takes place is referred to as the stage.
In order to keep track of how performers and set pieces more around the space, the stage is divided up into sections oriented based on the performers perspective to the audience. Movement is choreographed by blocking which is organized movement on stage created by the director to synchronize the actor's movement onstage in order to use these positions.
Note that for non-proscenium performance spaces, typically one direction is arbitrarily denoted as "downstage" and all other directions reference that point.
The house can refer to any area which is not considered playing space or backstage area. Outside the theatre itself this includes the lobby, coat check, ticketing counters, and restrooms. More specifically, the house refers to any area in the theatre where the audience is seated. This can also include aisles, the orchestra pit, control booth, balconies and boxes.
The areas of a theatre that are not part of the house or stage are considered part of backstage. These areas include dressing rooms, green rooms, offstage areas (i.e. wings), cross-overs, fly rails or linesets, dimmer rooms, shops and storage areas.