Normally the jargon of the story games community is a scene, sometimes a frame (for the comics games like With Great Power). Hearing "paragraph" triggered in me a thought about dividing a story game into paragraphs and dialogues.
A paragraph as analogous to an action sequence, with the focus on descriptions of what characters and things are doing.A game designed around this could use slightly different rules for each. A portion of game could be a Paragraph, with dialogue thrown in as flavour or for some small effect on the Paragraph. Players would describe what's happening and the rules would need to support the opposition between players for the outcome of the Paragraph.
A dialogue as analogous to improvised acting, with the focus on conversation between characters.
The other parts of the game would be Dialogue. This would allow the improv-minded players to shine, with opportunities for acting and silly voices. The rules would need to support the freedom of improv while providing a structure for direction or resolution (other than the players just shouting over the top of each other).
I'm not a clever enough designer to make this work just yet, but I can certainly see how both the Paragraph and the Dialogue exist already within games as styles of play. My Fiasco games tend to be heavy users of Dialogue, whereas my Fate games tend to be heavy on the Paragraphs.
I have a game scheduled this week with my regular group. I'm going to watch for Paragraphs and Dialogue, to see how our group plays and to watch how much Paragraph and Dialogue interact with each other.