What is the difference between the "3" and "D" on the automatic transmission shift lever on Toyota Yaris?

You'll have 1,2,3 and D. 1 restricts it to the equivalent of 1st gear, 2 restricts it to 1st and second, 3 restricts it to 1st, 2nd and 3rd and D gives it access to all the forward gears.

You'd use the "numbers" when you want to keep the gears low, for instance for engine braking on a steep hill or when you want to prevent it changing up any further perhaps for best acceleration and control. Putting it in D allows the transmission to make its own mind up.

Is it safe to shift from D to 3 or 2 and back while the car is in motion?

The D in the gear selector is Over Drive

commonly use 3 when towing trailer or boat.

"D" MEANS.....DRIVE BABY

"3"....STILL IN THIRD GRADE....HURRY UP YOU MISS THE TRAIN

AT YOUR DASHBOARD METER FUEL INDICATOR...."E" MEAN ENOUGH, "F" MEAN YOU'RE FINISHED