I have a cat and dog. I don’t think I’ve ever referred to them as “the cat and dog”.
It’s usually the fuzzies or the puppies The dog is elderly, so neither of them is a puppy. When I’m calling both of them to come in, it’s guys.
When I had 2 cats, I referred to them as the babies.
My two cats are the babies or the kitties. When I want to call them to their food dish (if I’m giving them a little fish, poultry, or meat), I call “Babies!” in a high-pitched voice.
Two shepherds, a schnauzer & a terrier here. Here goes my reputation as a hardass 
:
“The Goober Brothers” (the 2 sheps)
“The Pork Roll” (the overweight schnauzer)
“La Princesa” (my 14 year old terrier)
VCNJ~
My 3 rats - “The Girls”
My 2 lizards - “The Boys”
My cat and the fish go just by that - “The Cat” and “The Fish”. 
Well, three dogs, two cats and a cockatiel that all want dinner at the same time every night are usually referred to as the “various starving lifeforms.”
When dividing up the species it’s “all the durn dogs,” “GD cats,” and "freakin’ bird"respectively.
Our six cats are usually known as “the kittens,” “the kids,” or “the guys.”
For some unknown reason, though, they are also occasionally known as “the booguns.”
Dog and cat
“The Animals”
“The Angimules”
“The beggars”
I have two cats. They both come when I call “Kiddens!” Sometimes I will greet them individually that way, “Hey, kidden.” It’s not “kid’n”, it’s “kidden”.
No, I’m not calling them “kids”; the D sound is how my French grandmother always pronounces her Ts. I called the oldest cat that once when she was an only cat, my husband overheard and thought it was hilarious, and it just kind of stuck. They answer to their own individual names, as well - one won’t answer to the other’s name. But they both come running when I call out “Kiddens!”
Our three cats are most often referred to as “the kitties.”
Individually, we call them “baby”, and they seem to respond to it. They don’t know their given names at all, probably.
First thing when I walk in the house, and I know there are no other people around, is to yell “Kittens!”
So, collectively, they are “kittens” even though one will be 13 soon, another is a 5 year old fat beast and only one actually qualifies as a kitten. And he’s pushing it, having just hit 6 months.
Any of the following gets my two pugs running:
“Dogggieeeees!”
“Pooperdoopers!”
“c’mon you bottom feeders.”
I also refer to them as my “pugterage” since they insist on accompanying me just about everywhere.
“The kids”, as in “Have you fed the kids tonight?” or “Did you change the kids’ litterbox?”.
If they’re being rotten, it’s a collective “You little f*ckers!”.
E.
My god. That’s exactly how I refer to the little fuc…um…cats! It used to be “the girls” but now we have a boy, too…so it’s “the kids” or “the softies” or “the troublemakers” and sometimes…yes…“The Little Fuckers”.
Individually, I call them by their names or one of a dozen nicknames. The dog knows all his names (and responds to them), and all the cat’s names, (he’ll look at the cat or go find him.) The cat only responds to a couple of his names and only knows the dogs given name.
When I was growing up, we always had a bunch of dogs and cats around the house. My dad called them the Livestock.
Three guinea pigs, known as The Piggies. Or The Beasties. Or the Piggie-Beasts.
I know, I know, booooo-ring 
Dog and a ferret (more than one ferret at a time in the past).
We usually refer to them as the Animals, or the Beasts.
They both have their cages in a middle room that borders on the stairs. When I put them in their cages for the night and head upstairs to bed, I usually call out, “Good night, Beasts.” Or, alternatively, “Good night, Beast” (to the dog) followed by “Good night, Least Beast” (to the weasel).
When all of the animals I’m referring to are the same species, I use that. Otherwise, it’s generally “critters,” as in “It’s bedtime, are all the critters in?” or “Did you feed the critters?” I often make distinctions between the “indoor critters” (cats, iguana, dogs) and the “outdoor critters” (horses, goats, cattle).
The kids, the fuzzbutts, the girls. Today it was “the stinkbutts.”
“The Feline Biomass”. Or “The Cats”. The two males are “The Boys” and their nine month old irritant is “The Kitten”, and probably will be for the rest of her life, unless we bring home a younger one someday.
My mothers pets, which aren’t all the same species, are “The Critters”.