Yes. It's the same car.... '13 M3's are also available with 18's. Competition package has no impact on wheel fitment.
'04 E46 M3 - Jet Black - Sold
'08 E90 M3 - Alpine White - Sold
'13 E92 M3 - Silverstone II - Sold
'13 E92 M3 - Alpine White - Ohlins TTX, Fall-Line Suspension Arms/Bushings, AP Racing BBK, OE GTS Aero, Cobra Seats, Akrapovic GT4, GMG 4-point, BBS E88