Modern Square Dance has evolved overtime resulting in a standardized set of instructions or calls. This allows square dancing to be taught and danced alll over the world the same way. See Wikioedia: http://en.wikipedia.org/wiki/Square_dance
Round Dance is choregraphed ballroom dancing with 2 people (1 couple) arranged in circle around a hall. Dancers are prompted by a cuer to execute steps or figures in time with music. Social Round Dancing is organized with standard figure definitions. There are typically many couples in one or more circles all executing figures at the same time.
A square dance caller is the person who calls out instructions to square dancers.
A round dance cuer is the person who calls out or cues instructions to round dancers.