Domestic Keepers, or Barnyard Keepers, tend to be some of the newer keepers at the zoo, though some choose to stay there, or to transfer from other departments. They are forced to cope with not being taken especially seriously, as well as countless annoying jokes about what their animals taste like. This is further complicated by the fact that they are the keepers who are most likely to have to supervise visitor interactions with their animals, during which anything can happen. The most hands-on of keepers, they often develop some of the closest bonds with their animals, which is just as well, since from my experience domestics are the neediest of zoo animals - hoof trims, shearing, overeating, and to say nothing of the prevalence of hand-rearing.
Hoofstock Keepers, like Bird Keepers, often face the exasperation of working with animals that they love, but who visitors and other zoo professionals (including, alas, many administrators) can be dismissive of. When I started off in zoos, hoofstock keepers were often regarded as, there's no nice way to put this, the intellectually limited ones - good for shoveling poop and stacking hay, but not much more than farmhands (the same was often said about the Domestic Keepers... they also share a distaste for jokes about eating their animals). This really isn't true - hoofstock keepers are just as skilled as primate or carnivore keepers, and I've seen very impressive training and enrichment work from them. Because hoofstock collections in many zoos are in decline, the fate of many captive ungulates seems to be more and more in the hands of the private sector, which hoofstock keepers tend to work closely with. Certain other non-ungulates, such as kangaroos, capybara, ratites (ostriches and their kin), and even giant tortoises are sometimes deemed honorary hoofstock.
Carnivore Keepers can be somewhat prima donna-ish, having all of the glamour of working with the sexiest animals in the zoo. They also have to be perpetually on their toes, as more than one keeper has learned that complacency kills. Along with the primate keepers, they are among the most skilled in enrichment and training; their knowledge about animals in general, however, tends to be limited but very in-depth, as they usually work with a very small number of species, and a few individuals at that. Frequently exhausted by having to answer questions about whether or not they go in with the lions, polar bears, etc...
Primate Keepers take care of the most intelligent (don't tell the Elephant Keepers I said this) and personable (ditto) animals in the zoo. Their charges are, after all, primates just like them, so they relate more easily to them than other keepers would; in the case of great apes, you can easily start to think of them as people rather than animals. Just like people, however, many other primates are jerks, or conniving, or what have you, so primate keepers have to spend lots of their time getting into the heads of their animals. That also means that they have to spend lots of time analyzing and interpreting the complex social structures of their charges. The primate keepers would like to let you know that monkeys really, really, do not make good pets, so please stop asking where you can get one.
Elephant and Marine Mammal Keepers, while taking care of very different species, are going to get lumped together here. Both typically take care of one species (sometimes a small handful) and get to know their individual animals extremely well. Both care for the rock-star species of their facility, and in some senses the facility revolves around them (sometimes to the hostility of other keepers, who watch lots of time and money and resources pour into these animals rather than their own *cough, hippos, cough*). The bonds between keeper and kept are extremely strong, especially in cases where staff work free contact and their is nothing but trust preventing your elephants from picking you up and sending you flying three exhibits away. They tend to be the most outgoing members of the zoo staff, a handy requirement when your job requires frequent public demonstrations and keeper talks. Elephant and marine mammal keepers are the most frequently targeted by anti-zoo activists, which can make them highly defensive, especially in light of false accusations of how they care for their animals. At one facility where I worked, the one time I suggested that elephants might not be a good fit for our zoo anymore, I barely escaped with my life.
I didn't cover all possible animals, of course. Besides, the way zoos are arranged these days, it's common for keepers to care for geographic areas rather than specific taxa: one keeper might take care of jaguars, toucans, and anacondas as part of a rainforest section, maybe tossing some chow to the freshwater fish on their way down the hall. Still, even if you don't take care of a certain group of animals exclusively, you can still be on that "team." Though I work with a little of everything, and once wanted to be a Carnivore Keeper, I think of myself as a mixed reptile/bird keeper. Sometimes, when I talk with non-zoo friends (to the extent that I have any these days), I catch myself wondering... "What kind of a keeper are you?"
"And what about the aardvark keepers? Won't someone please think of the aardvark keepers?"