According to Merriam-Webster and the on-line etymology dictionary, ‘shindig’ evolved in 1871, from ‘shindy’, used since about 1821 to denote ‘merrymaking.’ A shindig refers to a lavish party with dancing, but I am impressed that in the new Lincoln movie Daniel Day Lewis is careful to refer to the White House party Mary Lincoln is planning as a ‘shindy,’ thus emphasizing the earlier form of the word. Possibly both derived from ‘shinny’ – used to refer to climbing, hand over fist, up a rope or, possibly the Scottish ‘shinney’, an early form of hockey. Neither of which explains how the term came to be applied to a party with dancing (modern hockey is more like a party with fighting).
Hootenanny, another of those nonsense words that took root in the American mind, evidently first appeared in the 1920s or 30s to denote any kind of unnamed or unnameable gadget – for which we now use the more prosaic ‘thingy’. In the 1940s, it came to be applied to an informal gathering of folk-musicians, presumably singing and playing, but not dancing – and, thus, not engaging in a shindig.
As for its application to folk-musicians, Pete Seeger, who must be an authority, says he first heard the word hootenanny used in the context of a thingy, for which another colloquialism at the time was ‘wing-ding’.
On the I Love Lucy Show (an uncommon etymological source, I admit) I distinctly remember Lucy and Ricky, with Fred and Ethel, singing ‘We’re gonna have a wing-ding’, to musical accompaniment while dancing – combining the best, one supposes, of shindigs and hootenannys.