Conformation is when the dog is evaluated for breeding based on overall appearance and structure based on the breed standard.
Agility is a timed competition where a dog and handler work as a team over and through multiple obstacles including jumps, tunnels, bridges and more.
Coursing agility trials are a timed event which judges a dogs ability to track and chase down prey.
Dock Diving is where dogs compete in jumping for distance or height from a dock into a body of water.
Barn hunting is a test of scent tracking. A dog has to use it's nose to locate a rat hidden in hay.
Obedience trials are where a dog must demonstrate the ability to walking politely, stay, retrieve, etc, all based on a command from their handler. These puppies would not do well.
Canine Good Citizen test is a certification program that evaluates dogs in simulated everyday situations in a relaxed, noncompetitive atmosphere.
Disc dog is just what you imagined. It's a competitive sport of fetch where dogs acquire points towards a title.