Paulster2 has the right idea but the best answer for BMWs is to look at realoem.com this provides a view into the actual BMW parts database. It also covers all markets, so you can easily figure out what parts are on your car and then by clicking on the part number it will show you all the cars where that part was used.
In the case of your ignition coil you will get something like this:
12137559842
Ignition coil
DELPHI
From:12/01/2012To:-Weight:0.250 kgPrice:
Supersedes:
12137638477 (04/01/2012 — 09/30/2013), Exchangeable retrospectively
12137594935 (01/01/2009 — 06/19/2017), Exchangeable retrospectively
12137582627 (07/18/2007 — 01/30/2009), Exchangeable retrospectively
12137571644 (12/01/2006 — 10/12/2007)
Part 12137559842 was found on the following E90 vehicles:
3' E90, 316i, Sedan, N43, EUR, (VF31) : Ignition coil/spark plug
3' E90, 316i, Sedan, N43, EUR, (VF32) : Ignition coil/spark plug
3' E90, 318i, Sedan, N43, EUR, (VF51) : Ignition coil/spark plug
3' E90, 318i, Sedan, N43, EUR, (VF52) : Ignition coil/spark plug
3' E90, 320i, Sedan, N43, EUR, (VF91) : Ignition coil/spark plug
3' E90, 320i, Sedan, N43, EUR, (VF92) : Ignition coil/spark plug
3' E90, 325i, Sedan, N53, EUR, (VE31) : Ignition coil/spark plug
3' E90, 325i, Sedan, N53, EUR, (VE32) : Ignition coil/spark plug
3' E90, 325xi, Sedan, N53, EUR, (VE51) : Ignition coil/spark plug
3' E90, 330i, Sedan, N53, EUR, (VE71) : Ignition coil/spark plug
3' E90, 330i, Sedan, N53, EUR, (VE72) : Ignition coil/spark plug
3' E90, 330xi, Sedan, N53, EUR, (VE91) : Ignition coil/spark plug
So, it looks like the coil is the same between both engines in Europe, but it also looks to be market specific. Don't take that a definitive, I had to make some guesses about your car to get there, and I might be starting from a wrong part.
BMW is all about reusing parts across their various product lines. I use this all the time when working on my older BMW to track down parts.