The term Costume Designer covers many different professions. For theater, it's called Costume Designer-Director or Set Designer-Costumier; for film and television, it's Costume Assistant or Costume Designer.
Most fall under the intermittent entertainment status. Depending on whether the costumes are created or produced, the functions are not the same. For example, the costume designer may create original costumes for fantasy films, science fiction or contemporary ballet... And for theater, film or television, the work is even more varied.