Choosing a collar for your pet can be a confusing decision. Collars can be used for identification and basic restraint, or they can be used for control while walking, or even for fashion.
Depending on your need, there are options for you to choose from. Simple dog collars come either with a snap and adjustable length or a buckle and size depending on where holes are, like a belt. These make up the majority of dog collars used, they are simple and do the job.
But those collars for dogs cannot be used on cats. Cats require a "break away" design for ID collars, so that if in their travels, the collar gets caught up on something, the cat is not strangled by its own weight. So, cat collars either have a snap that releases under pressure, or an elastic property that will either break or allows the cat to slide out of it. If you are interested in tying up a cat or walking it, then a harness is the proper choice, as it shouldn't strangle the cat in case of misadventure.
Collars can also be used to assist in controlling a dog while walking. The simplest form of this is a "choke collar". These chain collars work by physically placing a restriction on the neck as the animal pulls. For many animals, this level of discomfort is enough to correct the bad behaviour. These collars are meant to be used with a leash, they should not be worn 24/7 because they can accidentally choke the animal while it plays or sleeps.
Martingale collars are sort of halfway between a choke and a regular collar. They have a loop of chain and a band of adjustable nylon collar, so the "choke" is gentler, but still can be used for control.
More aggressive correction can be had using a "pinch choke" collar. These have prongs that give a greater correction when the animal pulls. These were primarily scary looking steel units, but recently plastic versions have been introduced that look and work a lot better. Properly used, even the most difficult dog can be controlled while walking with one of these.
There are a variety of other control "collars" that work in different ways, either using a head restraint, or something under the front legs, or even around the body. Not really collars, these control devices again are for use only when on leash.
Some pets get to dress up, sporting a little bling around the neck. Little dogs and cats with bejeweled, beaded, or weaved collars, large breeds with wide leather collars arrayed with studs or spikes, or even collars in your team's colours, the options are almost limitless. Breed specific collars for dogs with special needs based on the neck structure, like Greyhounds or Bulldogs, add to the diversity that can make collar inventory a retailers nightmare.
Regardless the species, breed or application, there should be a collar out there that fits your needs. Might take a little work finding it, but having the proper collar makes a world of difference for pet and owner.