Any object that an actor carries in his hand onstage is referred to as a hand prop -- books, bouquets of flowers, letters, lanterns and musical instruments are all examples of hand props. Actors may exchange hand props once on stage. The backstage technician in charge of properties, or the props master, must carefully monitor any props that change hands to make sure the props find their way back to the appropriate prop table for the start of each show.
When rehearsing for a show, the props master might pull certain items from a theater company's prop room to "stand in" for a necessary prop, until the show moves into the theater for technical rehearsals. Fake flowers might stand in for real flowers, or a generic newspaper or book might stand in for a specific edition that a performance requires. If a scene requires an actor to consume a prop such as food during the performance, then the props master will often use rehearsal props during rehearsal to avoid the expense of consuming real food over and over.
Props that "live" on the set are called set props. Set props are different from the set dressing in that actors always use set props. If a play involves a bar scene, for example, then the set might have glasses that are the set dressing and glasses that are set props both displayed where the audience can see them. Only the glasses that the actors handle are considered props. Set props include glassware, teapots, pens, pencils, paper and pots and pans.
A costume prop is a prop that "lives" on the actor's costume. This prop is not the responsibility of the props master but of the actor, who must make sure to set this prop on his costume before each show. Costume props include eyeglasses, wristwatches, hats and jewelry. If the actor wears a costume piece simply for decoration, then it is considered a part of the actor's costume. If the actor handles the piece in front of the audience, then it is considered a prop.
A prop is considered practical if it actually functions in the play. A gun that must shoot is a practical prop. A lantern or candle that must be lit is a practical prop, as are the matches or lighter used to light it. Real food that an actor eats is practical. This distinction is more important to the backstage crew and actors than the audience, since practical props must be replenished and kept in good working order.