Flat collar:
This is your plain collar designed to keep identification tags on your dog. It should fit snug, allowing 2 or 3 fingers slack. Not effective as a training collar but stylish. With long hair dogs, take care as the rubbing of the collar can cause mats.
Choke chain:
This has historically been the correction collar of choice for many trainers. It does what it says, it chokes the dog when the leash is pulled. Fitted correctly for training it should be snug just behind the ears. This collar is not safe to leave on your dog unattended if it gets caught it can strangle your dog. Also, studies have shown throat damage can occur even when corrections are given appropriately. It can be useful with a dog who can pull out of his flat collar easily due to a thick neck and small head, as the constricting of the choke chain will not allow the dog to pull out.
Harness:
A harness is specifically designed to make a dog comfortable while pulling. Widely used for sled and cart pulling dogs. Not effective as an obedience training tool however for breeds with thick necks and small heads it is a good place for identification tags. In long hair dogs, however, the harness will cause mats around the neck and under the front legs.
Prong/Pinch collar:
spikes prevent choking and throat damage but still cause discomfort the dog will work to avoid. Not to be left on unattended as the prongs can get hooked on things, particularly chain link style fencing or wire crates, causing the dog to become stuck and possibly panic and cause themselves harm. Fit should be snug behind ears for active training and can be looser in later training stages. Prongs should be long enough to rest on the skin, not on the outside of the coat. We recommend professional training before using this collar.
Limited choke/martingale collar:
Made typically of nylon with another nylon or chain loop that allows the collar to constrict like a choke chain but only allowing a partial choke. This collar should fit snug, allowing 2-3 fingers when not being pulled by the leash. Can be helpful as a place for identification tags for dogs with a thick neck and a small head. Also used on trained dogs who occasionally need small corrections.
Electronic/E-collar:
This collar gives an electronic static shock when a button is pressed. Useful in distance and leash free training with reliability. Used most often for field dogs. Can also add a beeper attachment used to give directional commands from a long distance. It is recommended that you seek professional training before using this type of collar.
Haltie/Gentle Leader:
Designed after a horse halter, and preferred by some trainers. This collar is sometimes useful in minimizing pulling. Many dogs will attempt to rub it off their face so neutralization training is often needed before use.
As you can see there is a great selection of collars to choose from. Ask your trainer or a qualified sales associate which one will be the best for you and your pet in training.