The terms "slow" and "fast" motion refer to the actual image as shown in projection (on the screen), not the recording or photograph speed.
In order to achieve the effect of slow motion, the camera must shoot faster than the standard projection speed. By shooting, for example, at 48 fps (frames per second), twice the standard speed of sound projection, the film will naturally take twice as long to be projected at standard (24 fps) speed. Therefore the movement will be slower. Two lovers, after a long separation, will race through a field of lilies to reach each other; in slow motion (projected at a slower speed than it was shot), each strand of hair and twist of the body will convey the strained effort the lovers make as they race towards each other.
The opposite is also true. By filming at 12 fps and projecting at the standard 24 fps, the film will pass through the projector at twice the speed it was shot; therefore the action will go faster. A clown falls down, shot at 12 fps, then jumps up again. Projected, the clown looks very funny, seeming to pop up like a jack-in-the-box, with little effort.
Just like long shot = comedy, and close-up = tragedy; so fast motion = comedy and slow motion = tragedy. ("Tragedy" being used in a more general sense of feeling or emotion, not necessarily of suffering.) Fast speed underscores motion; slow speed underscores emotion.
An analogy with sound speed might help. In the time of record players, most players had at least 3 speeds, sometimes four; 78 rpm (revolutions per minute); 45 rpm; 33 rpm; 16 rpm. 78 was used for the old breakable singles that were soon replaced by the 45 rpm singles in the mid-1950s (these were unbreakable); 33 was for the long-playing albums (12 songs); 16 was rarely marketed and was mostly for some spoken word albums, though experiments were made with symphonic music (three classical pieces instead of one could fit on a single 16 rpm disc). The trouble was, the slower the rpm the less the audio (sound) quality.
All of this is to discuss the main point: it was quite common, after playing 45 rpm singles to forget to change the speed, and play an LP (at 33 rpm), where the singer would sound like Mickey Mouse, because the speed would be faster than the speed for which the record was supposed to be played at. Or, the opposite, if a 45 were played at 33 rpm a female singer would sound like a man, much slower and deeper in sound. Just like a singer sounds more comical played at faster sound speeds, so a performer looks more comical shown at faster projection speeds; while even a silly pop song would sound serious or solemn if intended for 45 rpm speed but played at 33 rpm speed.
Finally, both record players and cameras were cranked manually at first ("hand-cranked"); so speeds were not perfectly standardized. In the case of movies, the projectionist could not be certain at what speed the camera was cranked and had to use his own judgment to compensate the difference or to add a difference never intended by the director (the projectionist might be sentimental and crank a love scene at slower speed, for example). Sound changed all this, since the speed had to be standard or the vocal quality would quickly change in timbre. 24 fps was chosen as the optimal speed for the quality of sound.
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