I believe that dramas are called plays because most of the times these dramas are written to be played on the stage or in front of the cameras for the television.
I had also once attended a comedy drama. Rather, this program was a series of short comedy plays. The drama was being performed live on the stage of the arts auditorium. The experience was thrilling. There was background music, but the music for the comedy play was not very important. The audience was also very hilarious, and they oft times broke into laughter as the comedy was ...