A reinterpretation is made on the basis of a previous piece, like a recreation, but with variations (eg. scene before / after, different characters or backgrounds, …). It can use the style of the new artist or mimic the one of the original artist. Some collectors are focused on a specific theme and commission different artists to give their own interpretation of this theme. See for instance these great "Trophy Wall" Themed Commissions on Chris C. CAF Gallery and this thread listing Themed Art Collections on CAF (alxjhnsn).