Contra Dancers: Usually a Ballroom-Hold Buzz-Step Swing.
American ECD: Usually a Two-Hand Turn.
eCeilidh (English Ceilidh): Usually either a symmetrical swing such as a Ceilidh Swing (especially for Hornpipe stepping) or a Ballroom-Hold Buzz-Step Swing.
Modern Western Square Dance: Ballroom-Hold with either short walking steps or a Buzz-Step. In my experience the walking step is by far the most common these days.
Traditional Square Dance: Usually a Ballroom-Hold Buzz-Step Swing.
Appalachian Big Set/Kentucky Running Set: Traditionalists use the Two-Hand Swing as described by Sharp; others use a Ballroom-Hold Walking-Step Swing, but hip-to-hip (as was collected by others); many modern American dancers use the Ballroom-Hold Buzz-Step Swing that they are familiar with.
Dancers in England (e.g. at Folk Dance Clubs and festivals): These are the most flexible, executing the Swing in a style related to the genre they are dancing, or following the caller's instructions, or just doing whatever they want for fun!
American Contra Dancers with experience in other genres such as "Swing Dance/Lindy Hop": Whatever they want! Not necessarily a Swing. They treat the 16 beats of "Balance & Swing" as "have fun with my partner", incorporating dips, drops, lifts, shimmies or anything else.
Beginners: Unless instructed otherwise, my experience is that they will take crossed hands and skip around. This is not a great swing; you are too far apart and you are not well connected. I would always recommend teaching them a better way to Swing or Turn.
Two-Hand Turns are often walked, though in a dance such as Childgrove, where you have to turn your neighbour one and a half times to change places, it is common to skip. Some dancers like to skip all the Two-Hand Turns.
When dancing a Contra Dance with a good partner and a "Partner Balance and Swing", I like to do a different Swing each time through the dance. I know twenty different holds, plus a number of interesting entries and exits.
Here are my Swing Workshop videos that explain all these types of swings, and teach you twenty different ways to swing,
In the pre-Playford Lovelace Manuscript, Trenchmore provides some stylistic information, a very rare thing in early documents: "then every man shall turne his mayde as long as he please, on way, and then backe agayine, the other way... Having soundly turned both ways, every man, with his woeman... and then all men and woemen turne round as before as fast as they can".
From this description it seems obvious to me that this was not a sedate Two-Hand Turn once around! They were Swinging. We have no idea what hold they were using. I know 20 different Swing holds; do we really think that the young, energetic, innovative dancers of the 17th century didn’t experiment with different ways to Swing or Turn?
It is possible to interpret the Trenchmore words as a stationary man twirling the lady under his arm, but, in the same document, for The Old Man with a Bed full of bones, it states "if you please, you may turne her arme over her head, and salute her". The twirl is explicitly described, so I assume that the Trenchmore words really do refer to a Swing.
Some people say that you couldn’t do a Swing close together until the second half of the 19th century because ladies' dresses were too wide. I don't believe that all dancers of all classes over the last five hundred years always wore clothing that prevented a Swing!
Energetic Turns were still being danced in the early 19th century; Thomas Wilson in "The Complete System of English Country Dancing" (1820) defines "Turn your partner" (page 9) as "join both hands and turn completely round to their places... with three Chasses Jetté and Assemblé". In simple modern terminology, and without 19th century styling, that would be three polka steps and jump.
And Charles Dickens says, in "Sketches by Boz" (1836):
"As to the gentlemen, they stamp their feet against the ground, every time 'hands four round' begins, go down the middle and up again, with cigars in their mouths, and silk handkerchiefs in their hands, and whirl their partners round, nothing loth, scrambling and falling, and embracing, and knocking up against the other couples, until they are fairly tired out, and can move no longer."
A good example of evolution is La Russe. The 1847 "set and turn" became "balance and swing partners" when it was published in ED&S in 1948, having been collected from the North-East of England earlier in the century; it was still danced there at the village dances despite having been forgotten everywhere else. On the "Here’s a Health to the Barley Mow" DVD you can see scores of dancers performing La Russe in 1950, all using perfect ballroom-hold buzz-step swings.
As for stylistic choice, have a look at this video of Mad Robin from 1695 (the dance, not the video!)
The original words are "turn hands" and "turn his Partner". Each couple chooses their own style. In the first swing of the dance the nearer couple takes a Double Allemande Hold, while the other couple takes a Ballroom Hold; both couples use a buzz-step. In the second swing the further couple takes a Two-Hand Hold to dance around twice. In the other set, while one of the couples just walks one turn, the lady in red takes a Two-Hand Hold and uses a buzz-step to get around three times!
This move is now known as Swing & Change and you can see it being danced in this video at 2:39 (they don’t quite complete the move in this example as they are changing formation):
Interestingly the Scottish have stayed with an intermediate version of the move. They still use a Two-Hand Hold and use a pas de basque step, but each couple rotates as they dance around the other couple. as in this example.
1651: Blew Cap (This is from a later edition of Playford; the original is just "Blew Cap".):
"the 2. man salute his owne and turne her".
1820: Thomas Wilson - "The Complete System of English Country Dancing". The first move, on page 9, is "Turn your partner" defined as "join both hands and turn completely round to their places... with three Chasses Jetté and Assemblé". The next move is "Swing round your partner" which is defined as a right-hand turn with the same footwork. There is a footnote: "The only difference between swinging and turning is, that swinging is always performed with one, and turning with both hands.".
Whether they crossed their hands or not is not clear, but there were references to a style that involved the arms curving downwards, with no pointy elbows, so it seems likely that one style was with the arms uncrossed (Chivers P101; Wilson P256-7).
First and opposite couples advance and swing round to opposite places
set and swing partners (Waltz Quadrille)
Set to Partners & Turn Partners
turn with both hands
the gentlemen turn the ladies quite round
All set and turn
1876: From a definition of Birling - a term used by the Scottish to describe a Swing:
"To revolve rapidly, whirl round, dance; to make a rattling or whirring noise."
1876 "He birled me roond like Nannie's wheel."
The first gent swing the opposite lady with right hand, then side lady with the left
turn partners with left hand
1909: In "The Country Dance Book Part 1" Cecil Sharp says, "To turn, two dancers face, join both hands, and swing once round, clockwise.". This is yet another example of "Swing" and "Turn" being used in the same sentence to mean the same thing.
1926: In "Good Morning" Benjamin B. Lovett defines "TURN PARTNERS" as "Lady and gentleman join both hands waist high and turn once around. To swing partners in the waltz position, the weight of the body of each should rest on the ball of the right foot, turning with the toe of the left." But dances also include instructions such as: "All swing partners with the right hand".
1939 In "Cowboy Dances" Lloyd Shaw refers back to Good Morning and Cecil Sharp’s Running Set. He uses "Swing your left hand lady with your left hand" and "Turn the left hand lady with your left hand" interchangeably.
For Swing he say, "each man takes his partner in a modified dance position, her right hand extended in his left, her left hand on his shoulder, and his right arm around her waist... With short steps the couple swings completely around twice in a "right about face" or clockwise direction.".