I actually get paid to get more people on bikes and in my time doing so, I've noticed a massive jumble of intermixed terms that give multiple impressions to different people. I'd like to know if/how your definitions of the following words differ from my own:
Bicycle: (According to the State of California) A bicycle is a device upon which any person may ride, propelled exclusively by human power through a belt, chain, or gears, and having one or more wheels. This, thus, includes unicycles, tricycles, surreys, etc.
Bicycling: The activity of riding bicycle. Regular trips too/from employment is referred to as "Bicycle Commuting"
Biking: (See "Bicycling")
Bicyclist: One who rides a bike. May also imply certain legal/safety views and/or preferences.
Mountain Biker: One who rides a mountain bike (typically off paved paths).
Biker: One who rides a motorcycle.
Cycling: The competitive sport of bicycle riding that implies the use of higher performance equipment and clothing than does regular bicycling. (Better explanation by chasm54 below)