I'll try and break it down.
Film content is usually (i.e. 99.9% of the time in my experience) stored on disc at 23.976fps, rather than at an exact 24fps. This is for technical reasons to do with the NTSC 60Hz, which is in reality 59.94Hz. Most people simply round up these numbers for convenience.
Most TVs are incapable of accepting a 24Hz input. In this case the player takes the 24Hz content and repeats frames to go to 60Hz, using the 2-3 sequence that's been used in DVDs for years. The process is called pulldown. Some TVs will accept a 24Hz signal, but they then convert that internally to 60Hz. In either of these cases you will see excessive judder on camera movements.
If your TV supports 24Hz material at a multiple of 24 (i.e. 72, 96, 120), then you will see a noticeably smoother image (not completely smooth, as there are still only 24 frames, they're just played in sequence rather than being repeated out of order). A lot of the newer, high end sets do this.
There's a Wikipedia artcile that explains in in more detail here : http://en.wikipedia.org/wiki/Telecine
Video content is normally laid to disc at its native framerate. While it is smoother than film, that's because it has more frames to begin with. Encoding a 24fps film (nearly all films are shot at 24fps) at 60fps wouldn't make it smoother, because the 60 frames would still only be made up of the original 24 frames repeated (which is how pulldown works).