In dog agility, what is a stopped contact and what is a running contact? Are there other types of contacts as well? Are the rules always the same no matter what venue you are competing in?
In agility the dog walk, teeter, or A-frame are types of contacts or contact equipment. The yellow at the ends of each designate the area that your dog must touch with at least one foot in order to have completed the obstacle successfully. These rules are in place for the dogs safety to ensure the dogs are not encouraged to jump from high heights on a repeated basis. All venues require contact with the down contact and the different venues have different rules about the up contact with the up contacts (for a list of the specifics see http://www.activedogsportstraining.com/files/Organiztion%20Comparison.pdf)
A "running contact" is when the dog runs through the ending contact area putting at least one foot in the yellow without stopping. For some dogs, especially smaller dogs, it can be very natural for them to always have a stride in the yellow but for dogs with a longer stride this is a trained behavior.
A "stopped contact" is when the dog stops at the end of the contact usually with their two back feet on the contact in the yellow and there two front feet on the ground in front of the contact. Some variations on this are a sit or a down at the bottom either still on the equipment or just next to it. For smaller dogs the teeter is a stopped sit or down usually because small dogs have a longer ride on the way down. You do not want a two on two off with a small dog on the teeter... the bounce can end up flicking them off if they only have two feet on and can create a (legitimate) fear of the teeter.