The first one does look like it acts as a martingale - I've never seen one like that before.
The second is the classic fur saver that everyone thinks of when you mention a fur saver. It was the collar required for SchH trials, and that is why everyone had one, and worked their dogs with it on. Though with the new rules, I believe a simple flat collar is allowed for trials also. For trial (and the AD), the leash goes on the dead ring of the collar, so it does not act as a choke chain.
The third one is a quick release, so that you can get the collar on without having to pull if over the dog's head. I can see that one being useful if you have a dog with a massive head and you would need a HUGE collar to get it over their head, and average neck size so that the collar would be way too big on them, or if your dog has issues with the collar going over their head (because of sensitive ears, maybe?). I don't know if that style would be allowed in trial though.
BH, OB1, TR1, AD
Rottweiler/Hairy Dog mix?? Shelter rescue
Gryffon Vom Wildhaus