In case of video, Higher-quality (high-poly) 3D models are used for the environment, characters and objects, also with spectacular special effects.
In Thief: Deadly Shadows this technique was changed, with some scenes fully animated 3D renders, others partially moving pictures, and pre-rendered videos. In Thief: The Dark Project, Thief Gold and Thief II: The Metal Age briefings consisted of panning and zooming sepia images with an accompanying voice and music track, whereas cut scenes were full color animations with some live shadow acting.
These are usually pre-rendered videos and/or real-time 3D graphics.
In the Thief games, the storyline is revealed before and after each mission was completed, using Cut scenes.