Character Study....

Inspired by reading springtime_gen signup posts and a bit of recent discussion...

What's your definition of 'character study/character exploration' as opposed to 'normal' fanfic? Is there a difference at all? And d'you have a story (read or written) that immediately comes to mind as an example?

*pets her shiny little triatha_ron bunny*
Now it just needs to hop the way I'd like it to ;).