Casablanca uses continuity editing in order for the scenes to flow seamlessly, so that the audience can focus on the story without interruptions.
For example, this scene in the film begins with Sam sitting down while speaking to Ilsa, then to a medium close-up of Ilsa encouraging Sam to play a piece of music. Another medium close-up is then used to show Ilsa’s disappointment when Sam turns down the request, although in the same shot Sam agrees to play the song. The film cuts between a medium close-up of Sam playing, a close-up reaction shot of Ilsa getting reminiscent and emotional, and a medium long-shot of Rick walking through the doors, getting annoyed and walking towards Sam. The intention here may be to show the audience how one simple thing can evoke different emotions for different people.