"Let Me Google That For You" is not an appropriate response here, because it's not a factoid question that has an obvious single page with the answer.
As @etale has found out, there are dozens of styles included under the umbrella of "swing dances". Most of them were (and often still are) regional, having evolved at a time when few people had televisions and long-distance travel was much less common than today.
Lindy Hop: Usually considered the original swing dance, though some older dances are now included in the umbrella. A fusion of Charleston, jazz steps, and other influences, it pretty much died out after World War II as the music changed. A few enthusiasts started a revival in the early 1980s, with a bigger revival occurring in the mid-1990s. Danced primarily to original swing jazz or modern songs in that style.
Balboa: A contemporary of Lindy Hop which evolved in crowded ballrooms in California while Lindy Hop was evolving in New York. Danced entirely in close embrace, with fancy footwork and rhythm variations but very little body motion. Modern Balboa is an amalgamation of the original dance (now called Pure Balboa or Strict Balboa) and the Los Angeles-evolved Swing (now called LA Swing as a separate dance, Bal-Swing as part of modern Balboa). Due to the small motions, Balboa is suitable for very fast music -- 220bpm is a comfortable social-dancing tempo -- but can be danced at any speed.
East Coast Swing: A simplified version of Lindy Hop formalized by American ballroom studios in the 1940s. Danced to original swing jazz, but also to early rock&roll.
West Coast Swing: An evolution of Lindy Hop which drops the Charleston kicks, is danced on a narrow slot, and substantially smooths out Lindy Hop's "bounce". It was stylistically very similar to Lindy Hop until the 1980s, but has dramatically diverged over the past 25 years. Currently danced primarily to Top40 / contemporary pop music, it is also often danced to R&B and blues. Nowadays it is also generally danced to much slower music than Lindy Hop.
Jive: A further development and codification of East Coast Swing by British ballroom studios. Characterized by "kicky" footwork.
Boogie Woogie: A European derivative of East Coast Swing danced predominantly to boogie woogie, rockabilly, and similar music. Originally 6-count moves only, but has in recent decades added back the Lindy Hop swingout and other eight-count moves. Characterized by moving the "bounce" from the body into the legs.
Rock and Roll: Another European derivative of East Coast Swing danced to rock and roll music. Has become extremely acrobatic, with followers doing mid-air multiple-rotation flips in competitions.
Collegiate Shag: Suitable for fast music. Like Balboa, it tends toward fairly small movements but is much bouncier.
Carolina Shag: An evolution of Lindy Hop danced primarily to "beach" music, and completely unrelated to either Collegiate or St. Louis Shag. Places a lot of emphasis on smooth footwork.
St. Louis Shag: looks like a cross between Charleston and Collegiate Shag Charleston: One of the pre-Lindy dances that are now included under the umbrella. Originally a solo dance, it is not uncommon to see a circle of dancers riffing off of each others' solo moves at a Lindy Hop event.
Other styles that I know little about: DC Hand Dancing (Washington, DC regional), Whip (Texas regional), Push (Texas), Modern Jive aka French Jive, Ceroc, Leroc, etc. (Europe).
I'll end with a crossover jack&jill competition that does West Coast Swing, Boogie Woogie, and Lindy Hop (in that order): (The first lead is clearly primarily a Boogie Woogie dancer -- a lot of BW legwork leaked through into the Lindy Hop.)
"Let Me Google That For You" is indeed not an appropriate response, for those too busy to look at the search results. Which return a link to a Wikipedia article with essentially the same level of detail if not more that what was just provided.
A style of Swing originally danced in a circular area to Jazz music using an OddEven-Qdd-Even rhythm (Lindy Rhythm) with nimble footed hops, skips, bumps, grinds, squats, and acrobatics.
A style of Swing originally danced in a circular area to Jazz music using an OddOdd-Even rhythm (Jitterbug Rhythm) with nimble footed hops, skips, bumps, grinds, squats, and acrobatics.
A synthesis ofLindy Hop and Jitterbug danced in a circular area using both Lindy and Swing Rhythm without the aerobatics.
A style of Lindy with hops and skips, and with the leader and follower remaining predominately in closed prom or closed open position.
A style of Shag predominately using Lindy Rhythm with the hops replaced with a slight body bounce, slips, and/or slides remaining predominately in closed prom or closed open position.
A style of Jitterbug originally danced to Rock and Roll music using Jitterbug Rhythm with delay steps on the odd units.
A style of Jitterbug originally danced to Rock and Roll music using Swing Rhythm with delay-steps, hops, and skips and avoiding aerobatics.
East Coast Swing
Another name for Lindy.
A style of Lindy danced to Country Western mUSic which emphasizes moving between double-hand-hold dance positions.
An upper-class English style ofLindy using Jitterbug or Lindy Rhythm with a an English Jive triple on the units. (What is an English Jive triple? A triple with the step (change ofweight) on the 1, a, and 2 beats, where 1 and 2 represent whole beats, and a represents three quarters of a beat.)
A Louisiana Bayou style of Lindy danced to Cajun music.
A Country-Western style of Cajun Swing.
DC Hand Dancing
A Washington, DC, style of Lindy which emphasizes moving between double-hand-hold dance positions.
A style of Swing popullar in the New York Savoy Ballroom in the 30s and 40s originally danced to Swing music.
West Coast Swing
A style of Swing emphasizing nimble footed rhythm breaks popillar in the California night clubs in the 30s and 40s and voted the California state dance in 1989.
A New Orleans, Louisiana, name for Swing.
A North and South Carolina style of Swing (the South Carolina state dance) where the leader and follower trade places on the track:, and emphasize the man's nimble footed rhythm breaks.
DC Hand Dancing
A Washington, DC, name for Swing emphasizing double-hand-hold positions on a revolving track and a whip left.
A Dallas, Texas, style of Swing which emphasizes spinning the follower between basket, vine, halo, and pin dance positions, using a double hand hold, push and pull leads (Double Resistance), and a rock rhythm break with bumps.
A Tulsa, Oklahoma, synthesis of West Coast Swing and Push.
A Houston, Texas, style of Swing which emphasizes spinning the follower between
A St. Louis, Missouri, synthesis of Swing and Lindy.
I would say that Ralf's post has the best information on the dances as they're practiced now, as in everything on there rings true to me as someone active in the lindy hop and swing dance world now (I also do a lot of balboa and have friends that are really into collegiate shag + know people who have done east coast swing, west coast swing and ballroom jive etc.
Balboa and bal-swing
Note that now "Pure balboa" is the stuff in closed position i.e. when the people are touching with their chests basically while balboa swing also known as bal-swing is what that dance is called when they break out into open and do the turns and stuff. These days balboa has lots of footwork variations and fancy footwork, slides and taps and small kicks
An amazing collegiate shag perforance, you can see that relatively still upper body and feet going crazy is common in both balboa and collegiate shag but the flavour and mood is very different. Also collegiate shag is utterly exhausting when danced with as much energy as in the clip, all the props to those dancers
Here's some fast lindy, you can also dance to slower music and the feel is quite different but it's all fun
One thing that's common with the swing dances is that they are mostly danced to swing music, like the three I've posted most about are all currently also pretty much always danced to swing music. Some of the other dances called swing dances used to be danced to swing music but the dance has changed over time and the music has changed as well and now rarely swings (west coast swing is a good example there). Note when I refer to swinging music I mean in a fairly technical way from a musicians perspective