"Sport" button/driving modes

[chris24]

Can anyone clarify the difference between what I've been told are 3 different driving modes on a (US) 4.8i with sport package (thus with adaptive drive):

1. Regular mode
2. "sport mode" - when you put shifter to left position, but do not manually shift it (just slap it to the left and leave it alone)
3. the "Sport" button.... behind the shifter

I was told the sport button allows extra air into the engine for increased performance, but have not been able to find any documentation to say what exactly it is for or how it relates to the adaptive drive.. Does the adaptive drive get activated by using that button or by putting the car in "Sport mode" when putting the shifter to the left position? Or does the sport button automatically get activated when putting it in that postion.......?

Thanks for any insights! The salesmen really seem to need more education on what they're selling.