Octopi aren’t fish.

Do you mean collective nouns ?

Or just “generic groups”, as in animal, plant, rock, fungi, lichen ?

Maybe group words that aren’t as specific as collective nouns and not as generic as groups:

• canine
• marsupial
• mammal
• primates
• carnivores
• vertebrates
• reptiles
• birds

Does that help?

Well this was a fun game to play with the family. Here's some words we came up with:

Algae
Amphibians Animals Annual
Aquatic Baby Bacteria
Beasts Bipedal Birds Blossoms Buggers Bugs Bushes Cacti Carnivores Cats Crabs Crawler Creatures Creepy-crawly Critters Critters Dogs Dolphins Domesticated Estuarine Fauna Fern Fish Flora
Flutterer
Flyer
Foliage
Forager
Fowl Fungi Furballs Game
Grasses Herbivores Herbs Insects Invertebrates Larvae
Lentic Lichens Lizards Lotic Mammals Marine Microbes Mini-beasts Molds
Moss Moths Nestling
Old Omnivores Pelagic Perennial
Pests Plankton Pond dwellers Pray Predators Primates Protozoa
Prowler
Quadrapedal Reptiles Reptiles Riverine Rodents Scavengers Seedlings Serpents Sharks Shelled Shrubs Spores Swimmer
Symbiotes Trees Tropical Varmint
Vertebrates Vines Viri
Weeds Wetland Whales Wild Worms Yeasts Young xerophytic

Hope that was helpful.

You want broad sweeping categories? Maybe categorize by behaviour?

Crawlers Slitherers Swimmers Flyers Stationary creatures Sunlight eaters Carnivores Plant eaters Omnivores

I think decide what your groups actually are first, then label. So a fish in this list would be swimming carnivore.

Fish: anything that swims

Bird: anything that flies

Floof: anything small and furry

Behemoth: anything large and stompy

Leviathan: anything large and swimmy

Beast: anything big and bitey or not otherwise categorized

Reading the comments on this makes me realize how often we think about animals, considering we apparently have thousands of different ways to categorize them, even if it's more by vibe than anything else...

So it sounds like you could make categories that are

• location based: sky (flying), jungle
• climate based: ice/cold, desert
• task based: tunneling animals, builder animals, nest making animals

You could also start from a list of animals and then categorize them afterwards based on what you have. As for a list, maybe by biological families or classes?

https://en.m.wikipedia.org/wiki/List_of_animal_classes

And here we thought baraminology would never be useful for anything.

Canid and canine generally mean any of the dog-like animals: domestic dogs, wolves, fox, coyotes, dingoes, jackals, wild dogs

Parrot applies to members of the Psittacine family: parrots, macaws, parakeets, cockatiels, cockatoos, parrotlets, lorikeets

Herps and herpetofauna are used to collectively refer to amphibians and reptiles: frogs, salamanders, newts, lizards, turtles, snakes

Bear means all actual bear species but is also often used in reference to pandas and koalas (just don’t say it in front of my scientifically accurate kid)

Waterfowl is ducks, geese, swans

Depending on why or how you’re using categories, you can also group by characteristics: Do they have fur, feathers, or scales Do they lay eggs or give birth Are they predator or prey Do they eat meat, plants, fruit, pollen, or some combination

The biggest difficulty with answering this question I think is that I don't know how broad the categories should be. Do you have an estimate of how many categories you're looking for?

Collective noun might be the word you're looking for. This list is for animals in particular.

I know there are other casual-usage words for big categories of critters

And that's the only word you need, right there.

IDK any list like that. Why not make the list in your own language and see how much can translate to English without distorting the meaning too much?