A storey (Australian English, British English, Canadian English, Indian English, New Zealand English) or story (American English) is any level part of a building that could be used by people (for living, work, storage, recreation, etc.). The plurals are "storeys" and "stories" respectively.
From http://en.wikipedia.org/wiki/Storey
Story, a recounting of a sequence of events
From http://en.wikipedia.org/wiki/Story
Story, plural stories also storeys
The space in a building between two adjacent floor levels or between a floor and the roof
From http://www.merriam-webster.com/dictionary/story
Story, plural stories
An account of incidents or events
A statement regarding the facts pertinent to a situation in question