Hello Terry,
I'm in your area and teach each of these arts. I should come visit sometime and I could demonstrate the differences.
Similarities: The one thing that all martial arts have in common in they are practiced by human beings. Naturally, humans are bound by the mechanics of the human body. Going outside of this range usually results in an injury, whether sudden or progressive. In normal activities (outside of martial arts), everyone walks, runs, twists, swings their arms, etc. These same motions form the foundation movements of all techniques in martial arts - no matter which "style" is practiced. You can apply the same walking motion used for normal getting around as a knee strike, front kick, even stomping. Running (with the arms) is the same motion for punching in front or elbowing behind you, etc.
Differences: For Tang Soo Do and Taekwondo, not really that many differences - just the emphasis of the training and curriculum. Hapkido and TKD/TSD, many differences - easier to demonstrate than explain in text.
R. McLain