Yes, the design of a paper airplane will certainly determine its distance and speed along with accuracy and stunt performance!
Larger planes with larger wing designs will fly fastest, and these are also best at hitting targets.
Obviously a steady hand and throw will make a difference too, it's all about aerodynamics and gliding your hand a certain way will determine speed and distance of the airplane. It's all about trial and error.
Another factor is that when the plane opens up during flight the air slows it down somewhat, so stapling it closed can help.
You also need to deal with the balance of the plane to make sure weight is evenly distributed. We have all made planes that nose dive about 6 inches from where we throw them :-)
I have added a video below which will demonstrate where to staple and tape the paper airplane - have fun making it!
A strange fact for you too - on a windy day, an unfolded (normal) piece of paper flies farther and faster than any folded paper airplane!