When a dog is being trained it is customary to use what is called a training collar or martingale collar. Unlike regular collars that are sized to fit the dog's neck, training collars are designed to afford more comfort to the dog by using two loops to circle the dog's neck and provide a pressure gauge for the loop to keep a dog from pulling away. A regular dog collar usually slips off during training because dog's are usually pulling backwards when being taught and unless you have a collar on so tight it is restricting the dog's breathing a collar won't stay on very long.
Sometimes a dog training collar is confused with a choker. A traditional choker is a chain collar that employs the "jerk and praise" method of training which is generally discouraged due to the damage it can do to a dog's neck, back and tracheal injuries. A dog training collar is designed to gently tighten when a dog pulls so it can learn on its own not to try slipping out of a collar. In addition to preventing injury to your dog, a more restrained training method will also encourage better, less aggressive behavior from your dog so he is more adaptable with crowds, families and children.
You can also find training collars that are referred to as head halters and gentle leaders. If you have a dog that is prone to pulling during walks a head halter can help discourage a dog from pulling on a leash during walk. The halter fits under the dog's eye which, unlike a muzzle, still allows him to bark, sip and eat but will force the head up if the dog tries to pull too hard on a leash. Not always recommended due to the dangerous design of the device, head halters are often best used by professional dog trainers or people who have more experience with dogs since there is a chance of neck or back injury if one is not used properly.
The same is true for electronic and shock collars. While these gadgets might be popular and trendy most trainers agree that "stun-gun" type collars are not a good way to train a dog and often lead to aggressive and unpredictable behavior. If a dog is doing something out of fear rather than respect you can't always predict the outcome. Shocks and stimulations can have detrimental effects on a dog's behavior and cause erratic situations in the future.