The names Bimmer, Beemer or Beamer refer to BMW vehicles. Bimmer is the correct term for BMW cars, while Beemer and Beamer are the terms used for motorcycles.
BSA was one of the big motorcycle brands that existed when BMW emerged in the motorcycle industry. Since BSA motorcycles were popularly known as Beesers, BMW fans decided to call BMW motorcycles Beemers. Overtime, the spelling Beemer got mixed up as some people started using the term Beamer instead of Beemer.
BMW car enthusiasts wanted a new term to differentiate from motorcycles and came up with the term Bimmer.