Round dancing consists of one or more couples, dancing in a circle. Round dancing is similar to ballroom dancing except that dances are cued. Round dancers do foxtrots, waltzes, two-steps, rumbas, jive, etc.
In (Modern Western) Square Dancing, a caller gives the commands, which the dancers must execute. The caller gives them in whatever order he chooses. The dancers do not know what is coming next.
In Round Dancing, a cuer delivers a pre-choreographed dance for each piece of music. The choreo for that music is the same each time.