Basically, formatting styles are only used in general text, script styles are only used in Scriptwriting Mode.
Formatting Styles are used for quickly applying a set of formatting options to a selection of general text. So, for example, you could select:
This is a Heading
and apply the Heading style preset (Format > Formatting > Apply Preset > Heading) style and it will turn the selection bold, increase the font size and so on.
You would normally ONLY use formatting presets (styles) in general text, not in Scriptwriting mode.
Scriptwriting mode is special because it allows you to use the Tab and Enter and other keys to format script elements easily. For example, on a new line press tab and it may automatically put you into dialogue mode with the character name centred and in capitals. Press enter and it will indent the next line for the dialogue, and so on.
Of course, different types of script require different settings (film scripts are different from UK stage plays, for example). When you choose one of the styles in Format > Screenwriting (e.g. Screenplay, Stage Play etc), you are essentially telling Scrivener what to do when you press Tab, Enter or other shortcuts in Scriptwriting mode (and only in Scriptwriting mode).
If you open the Script Settings… dialogue, you can see which script elements are available in the currently selected script style: and you can then edit their format and behaviour, or create your own.
So if you want to create your own scriptwriting style, then
a) Select the script style (nearest to the one you want to create) in the Format > Scriptwriting menu. You will see that the first item changes to reflect your choice e.g. ‘Script mode - Screenplay cmd-8’.
b) Try out the various elements (Screen Heading, Action, Dialogue etc). If you want to change any of the elements then open the Format > Scriptwriting > Script Settings menu and make the changes there.
There’s quite a lot to all this, but it’s fairly intuitive once you’ve played around with it for a bit and it’s explained well in the manual.
Hope this helps…