How does an aircraft taxi?
Aircraft are not always moved with tugs (the small vehicle you refer to). Much of the time, they operate under their own power.

Airliners are generally pushed back from the gate using a tug, as that's the simplest and most efficient method. They then taxi to the runway (and all the way up to the gate, after landing) using their own engines to provide thrust. This is true of both jets and propeller aircraft.

Some work is being done on self-contained electric-powered ground propulsion; one major player in this area is a company called WheelTug. They use high-torque motors and the aircraft APU to allow the aircraft to move itself without starting its engines or requiring a tug to be connected and disconnected.