I see that cowgirl and ranch-hand Kristen gave you a pretty good answer when she said movie writers are called screenwriters and the materials they produce are called screenplays (and I have a background that includes ranching, as well, so I hate to contradict her), but the real answer to what movie writers are called should be moviests.
What? Huh? You don't buy that?
Okay, then go along with Kristen. But, remember I leveled with you!
Alright, you caught me. Actually, the truth is that the writer of a film script (no one actually writes a movie, which is a visual collaboration of the filmed version of a written story) is indeed called a screenwriter or, less frequently and less precisely, a scriptwriter. And what he or she writes is indeed called a screenplay (or script, for short).
The difference between the two is that the name screenwriter applies to someone who writes only screenplays for the "big screen" (i.e., movies or films). Meanwhile, the name scriptwriter applies to someone who writes scripts for any type of production vehicle, including radio, video, business or educational presentations, podcasts, and so forth. So, while all screenwriters are scriptwriters, not all scriptwriters are screenwriters.
Got that? Good.
By the way, not that you asked, but a scriptwriter for a theatrical production such as a Broadway, dinner theater, or even school play is called, of course, a playwright, differentiating that type of writer from scriptwriters for any vehicles outside of the stage.
Got that, again? Good, again.
Oh, hell. On second thought, just forget about all that nonsense and go along with Kristen's definition. After all you can't doubt the word of a cowgirl and ranch-hand. Trust me on that.
Smoke if you've got 'em.
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D. J. Herda is author of the new ebook series of writing advice, About Writing Right, available at amazon and at fine booksellers everywhere.