"Script" and "Screenplay" are exactly the same thing. A "play" is something
performed - the "screenplay" is a word limited to a script for the screen. The
"teleplay" is a word limited to a script for the television. "script" is the word
used for everything - a speech, a computer program, a set of papers. So you
can write for the stage and call it a script, you can write for TV and call it a
script, you can write for movies and call it a script.

The "story" is the series of events that happens. A story can be in a novel, a
play, a TV script, a movie script and told without writing at all.

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The aim of an argument or discussion should not be victory, but progress.
Joseph Joubert, essayist (1754-1824)

In other words, 'screenplay' is the most precise definition of a dramatic text written for screen. Most often, it specifically means big screen (as in movie theatre), as opposed to the TV screen; as CI mentioned, 'teleplay' is the word that is often (but not necessarily always) used for a dramatic text written specifically for television. 'Play' refers to any text that is to be performed (usually, on stage). Story is exactly what it means (for example, what your mother read to you at bed time), fictional narrative, without any specific target medium.

So, you have:

Play
Screenplay
Teleplay

Where the difference is in what the target audiences are.

A script can be for any of the above: a movie, TV movie, 1-hour TV drama, 30-minute comedy, 15-minute short, 30-second commercial, 3-act Broadway musical, as well as for non-visual media (radio, podcasts, etc).

When a screenplay is delivered in a script form, that usually means that some specific set of rules is followed regarding the formatting of such text (i.e. use of specific typeface, text margins, text indentations pagination, etc). In most countries of the world, there are more or less specific guidelines for such format. US (i.e. Hollywood) has quite strict rules regarding script format for screenplays. These rules make it simple for everyone involved in the production to follow the script. Another consequence of those rules is that, on average, one page of script formatted according to the Hollywood guidelines results in approximately one minute of film time. This makes it easy for writers, directors, producers and all others involved to figure out how long is the movie going to be (as well as how long are individual acts, scenes, etc.).

So, and example of a story would be any fictional story published in, for instance, The New Yorker magazine ( http://www.newyorker.com/fiction/features/2010/11/22/101122fi_fiction_doctorow), or the story of Cinderella, or the story of a Boy Who Cried Wolf, or any other possible fictional story you could think of.

A screenplay, based on a story by Sir Arthur Conan Doyle, about Sherlock Holmes, here available as a script, in Hollywood formatting:

http://www.mypdfscripts.com/download/726

Story is the loss of your State of Perfection and return to it.

Screenplay is the blueprint that will layout your story in a way that makes it filmable.

Screenplay Structure: http://www.clickok.co.uk/index4.html
Online Formatting: http://www.plotbot.com/
Formatting Software: http://www.finaldraft.com/

I recommend these two resources for aspiring Screenwriters for the absolute BEST guidance that assumes you are just starting out but want to go far: 🙂

www.wordplayer.com

http://www.amazon.com/Film-Scriptwriting-Practical-Manual-Second/dp/0240511905/ref=sr_1_1?ie=UTF8&s=books&qid=1290787236&sr=8-1

Brian Dzyak
Cameraman/Author
IATSE Local 600, SOC
http://www.whatireallywanttodo.com
http://www.realfilmcareer.com