What’s the difference between the two forms?
In movies, directors and producers are allowed to change the script, sometimes drastically. They can even put out multiple versions of the same movie. What they are crafting as artistans is the final experience of watching the movie. The writer of the screenplay works within this overall purpose. His screenplay does not exist as a distinct work of art, but is rather one step, literary but fluid, toward the real work of art, which is the movie as experienced by the consumer.
The case of the stageplay is somewhat different. Each production is an ephemeral, subjective representation of the stageplay, which is published in book form because it is considered a solid independent literary work of art.
The difference isn’t absolute, because even in the case of the stageplay, it has failed as a work of art unless an audience views a production of it on the stage. (It may have failed as a work of art even then, but anyways…)
However in the first place the script generally serves the production while in the second the production generally serves the script.
Why did it turn out this way? Possibly because Shakespeare, whom we know only through his treasured and revered scripts, towers over the playwriting scene to this day, while in the genesis of the moving picture, it was studio executives who dominated everything.
But it’s also because of the nature of the thing. A movie only needs to be produced once, but that one production is recorded and becomes the movie ever after, watched over and over again by millions of people. The stageplay continues to exist in script form, being produced over and over again, differently each time, by companies of greater or less abilities and funds and creativity and skill. One production will never suffice because it’s presented to an audience, not a camera; the script outlasts the production.