The pilot of the Pilatus reported that, after the local air traffic controller gave him an instrument flight rules clearance, he taxied the airplane from the ramp to the taxiway. While turning onto the taxiway, the controller instructed him to give way to an airplane on the same taxiway. He acknowledged the instruction; stopped the airplane; looked left and saw a Cessna, which had already passed him. He then looked right and did not see any other airplanes on the taxiway and continued to taxi. Shortly after, he realized that the airplane's propeller had struck something, so he immediately shut down the engine, deplaned, and realized that he had struck another Cessna that he had not seen. The flight instructor in the Cessna reported that, while the student pilot was taxiing back to the ramp, they were instructed by the local air traffic controller to follow company traffic while passing another airplane to their left, "holding" short of the same taxiway. He then looked left outside of the window and saw a spinning propeller moving closer toward the airplane. He immediately grabbed the controls and hammered the right pedal, but the other airplane's propeller struck their airplane's left wing. The Pilatus sustained damage to the propeller. The Cessna sustained substantial damage to the left wing. The pilot and the flight instructor reported that there were no preaccident mechanical failures or malfunctions with their airplanes that would have precluded normal operation. A video provided by the airport authority showed that the Pilatus taxied left onto the taxiway from the ramp without stopping and that there was another airplane farther down the taxiway.