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There are several differences between men's and women's gymnastics and also between artistic and rhythmic gymnastics. All the divisions have several similar base concepts, but that is practically all that is alike.
Women's gymnastics is not like softball or women's basketball where it's the men's sport modified for women. It's completely different, starting with events.
Men compete on parallel bars, high bar and pommel horse while women compete on the uneven bars and balance beam. The only overlapping events are vault and floor. Women use music for their floor routines but men do not.
Men's routines focus on strength and power while women's routines are more focused on artistry and strength (though those factors do come into play for each team).
Every rhythmic gymnastics routine is performed to music and they do not use any special apparatuses, instead everything is done on a padded floor surface. Rhythmic gymnasts use props like a rope, hoop, ball, clubs and ribbon.
In team competition, artistic gymnasts perform one at a time while rhythmic gymnasts compete as a group and are judged on their synchronization.