When is a remake not a remake?

The Coen brothers' True Grit starring Jeff Bridges and Matt Damon may be regarded as a variant on Henry Hathaway's True Grit starring John Wayne and Glen Campbell, but as far as I'm concerned it is something much more than a remake. So just what is it that distinguishes a fine new retelling of a forty-year-old Western from a mindless American remake of a Swedish vampire movie, say?