In actual fact there is 'St Louis Shag', 'Carolina Shag' & 'Collegiate Shag' - each of which are thought to be completely unrelated dance styles.
Carolina Shag is a lead oriented dance where the leader "peacocks" a variety of complex improvisations, while the follower performs subtle (or no) footwork variations.
St. Louis Shag seems to be more closely related to the Lindy Hop break away - its a fast dance style, but seems ultimately to be quite limited.
'Collegiate Shag' is by far the most common 'Shag' - the upper body and hips hardly move as the legs do convoluted kicks and fancy footwork 'slow, slow, quick, quick...' Its an impressive dance style and works especially well to fast tempo music.
This is what wikipedia says about Collegiate Shag
Some nice clips of various Shag styles
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