Kick start means to start the engine of a motorcycle by stepping very hard on the kick starter. It also means to provide motivation to start or restart an activity.
A. "The thief kick started the motorcycle and took off."
B. "A large construction project is more than enough to kick start the economy."
Jump start is a method of starting a motor car when the engine does not react to ignition in the normal way. The car is pushed freewill down a hill where the gears are suddenly engaged.
"Have you tried jump starting the vehicle?"