As the 19th Century drew to a close, the dances of the Victorian era were losing their edge. Dance enthusiasm was waining. Hostesses were complaining about men who would come to a ball and spend the whole time outside smoking. The dance world was hungry for something new. That something was the new and exciting syncopated sound of Ragtime coming out of the African American communities up and down the Mississippi from St. Louis to New Orleans. From thence it spread across the US and then to the world.
This new syncopated rhythm demanded new dances and a new, modern approach to dancing. It started with the Cake Walk. The Waltz remained, but it changed with the time, morphing into the Hesitation and the Boston.
The Quadrille and Polka faded away, and the dominant dance of the turn of the 20th Century was the Two-Step, which was more or less a Polka without the hop, but which was danced with a very different affect. Dance cards of the time were often nothing but Two-Steps and Waltzes.
As fashions changed, tbe Tw0-Step gave place to the Turkey Trot, then the One-Step and then the Foxtrot, but all of these dances were danced to the same 4/4 rhythm. They could all be lumped under the term, used at the time. of "Ragging dances", and I submit that they are all, in fact, just facets of the same dance.
On the same dance floor, one couple could be doing a Two-Step, another a Turkey Trot, another a One-Step and yet another a Foxtrot, all to the same music. Further, any couple could easily slip from, say, a Tw0-Step to a One-Step and back again, to suit their mood. To think of each of these, as well as the numerous novelty dances (Grizzly Bear, Camel Walk, etc.) as distinct and different dances, like the Cha-Cha or Quickstep are today, is to miss the point. They were all points on a continuum and all just different ways of doing the Ragging Dance.
There is a timeline for when various variations and stylings were more or less popular, but there are no clean breaks. There were plenty of people who wanted very much to police the dancefloor and regulate and codify the actions of dancers, but no one ever came close to succeeding. It was a jungle out there.
I will also discuss Latin America's contributions to the collection of "Modern Dances": the Tango and Maxixe.
Here's a video discussion of the topic.