The answer to this question depends on if the play is being read or if it's being staged. The latter is its intended purpose, so I'll focus on "live drama" versus "fiction."
1. Live drama uses a live audience. Actors on stage feed off the energy in the crowd, and intensifies the mood. Fiction has readers, but no live audience.
2. Live drama is more fluid and easily revised; novels and short stories are fixed--cannot be changed. The director of a play can take out a line or even a scene if it does not work from performance to performance. A fiction writer cannot revise so easily or quickly.
3. Live drama is collaborative; fiction is solitary. In drama, there are actors, directors, and choreographers, musicians, and techs. It's obviously much more of a team production. Fiction is composed in solitude.
4. Live drama is meant to be heard and seen, not read. Fiction is obviously meant to be read. So, drama is a audio-visual performance-based art, and fiction is much more contemplative.