The word "premium" has nothing to do with the quality of the fuel. It's just a sales gimmick that gas stations use to try to get people to buy the more expensive stuff. The only real difference is the octane rating, which is what that square yellow sticker that displays a number from 85 to 95 shows. The higher the octane, the more resistant the fuel is to combusting spontaneously. Many high performance engines require premium fuel because they have higher compression ratios than normal, mundane engines. High compression means more heat and pressure is generated, which regular unleaded fuel could spontaneously ignite under before the spark plug fires, causing a condition known as detonation, which can severely damage the engine internally. If you did fill up with premium just once, it's not a big deal. Your fuel economy will be slightly reduced and you may even have slightly reduced power depending on the engine nomenclature. The manufacturer of the vehicle, whether it be BMW or Chevrolet, makes no difference to the fuel requirements of the engine unless specifically stated so by the manufacturer for that particular vehicle.