just wondering if there are different types of cocci (species specific) or can one animal catch it from another species droppings? (mainly referring to rabbits, guineapigs, turkeys and chickens)
No, cocci is species specific. Chickens, Turkeys, and other birds can share cocci, but rabbits, guinea pigs, dogs, cats, etc can't catch cocci from birds. I work for a vet, and a few years ago we had several dogs who had some "weird" looking cocci in the stool samples they brought in. We sent the samples to an outside lab with more specialized equipment/techs and it came back as "pass-through" rabbit cocci. We were seeing it in the dogs' stools not because the dogs had cocci from the rabbits, but because the dogs happened to eat some rabbit poop from rabbits that were infected with cocci. The rabbit cocci did not cause any problems in the dogs and did not need any treatment.