The Ballroom (or standard) dances are romantic, jazzy or passionate. In competitions, the man wears a white bow tie and tailsuit and the lady usually wears a long, floaty dress to best show off the spins around the floor. All the dances are "in hold" which means the lady stands close to the man and the couple dance as a single unit.
The Latin dances are cheeky, fiery and fun. In competitions the man might wear an open-necked shirt and the lady will usually wear a short dress as these dances come from hot places like South America! Partners don't have a fixed hold - they can dance side by side, for example.