Step dance is the generic term for dance styles where the footwork is the most important part of the dance. Body and arm movements and styling are either restricted or considered irrelevant. Step dances are usually solo or group dances.
Step dance is one end of a spectrum of dance styles. The opposite extreme is Formation dances (eg Square dance), where the movement patterns around the dance floor and armwork are the most important factors, and the footwork is very simple. Most social dances fall between these two extremes.
There are very few pure step dances, as most include at least some upper body or arm styling. Often step dances performed in shows add elements of show styling, which can bring them into conflict with the traditionalists.