These are the protective plates as you open the door, you see on the sill. I have one set off mine, and another from an E89, but they both are the same fitment. The E89 ones are all black, and will get some pics up tomorrow.
Top ones are aluminium that are standard in the Z4, and the bottom ones are plain black, which are from the E89. They look better IMO, as the others don't match anything else really.