Registration is a method of officially recording something. Usually something is registered to claim more rights, or to protect ownership, or because the law says it must be registered to be used legally.
A register was a large book. It was used like a diary to record business dealings or other events.
Reasons for registration [change]
Motor Vehicles are registered to prove who owns the vehicle. Cars or vans that not registered cannot be driven on roads. Aircraft not registered cannot be flown. Proof that a vehicle is registered is the number plate or licence plate. Vehicles must also be registered before they can be insured in case of an accident or in case of theft.
People who stay in a hotel register their names and addresses when they arrive. The hotel can then workout how much the people most pay for their stay. The local police may also keep a copy of these names to help fight crime.