I am a Round Dancer and have talked with a number of Ballroom Dancers. One primary difference is that there is no competition in Round Dancing, even at the highest levels. People Round Dance for their own enjoyment. The steps in both are similar and many are identical. Watching ballroom dancers has convinced me that, while the steps and figures are identical, the styling is occassionally slightly different. Round Dancing is usually described as "Choreographed Ballroom Dancing". That is, someone writes Ballroom steps to a piece of music and distributes a "Cue Sheet" to Round Dance Cuers. Cuers all over the world then "cue" the dance and the dancers do the steps and figures. There is no memorizing of each dance and many songs have multiple dances choreographed for them. There are over 25 different rhythms taught in Round Dancing. Each rhythm is separated into "Phases" with the easiest steps being Phase 1 and the most difficult being Phase 6. Round Dancing has been under the auspices of Square Dancing for decades. Chances are, if you go to a square dance, the caller will call 2 squares, then a cuer will cue 2 Round Dances. Most Square Dance Clubs have Round Dancing and there are a number of clubs that are Round Dance only. The clubs that have Round Dancing usually have club sponsored classes. Many Round Dancers dance at the lower levels only and are not interested in spending the time necessary to become as good as most serious Ballroom dancers. They do it for fun only.
For more info see http://www.roundalab.org/
Hope this helps.