Yes. It's the same car.... '13 M3's are also available with 18's. Competition package has no impact on wheel fitment.
'08 E90 M3 - Alpine White - Sold
'13 E92 M3 - Silverstone II - Sold
'13 E92 M3 - Alpine White - BBS E88, JRZ, Akrapovic, AP Racing
'04 E46 M3 - Jet Black - BBS E88, KW Clubsports, Brembo BBK, SuperSprint Exhaust, Recaro - FOR SALE