hmm
i think this would depend on the aliens actually, but ill take a shot at this.
assuming they categorise based on physical features i think it would be pretty similar, maybe with the largest groups below plants/animals being legs vs. no legs- so mammals, most reptiles, birds, insects, etc. in one, and fish, snakes, legless lizards, aquatic mammals, mollusks, etc. in the other. i think anemones, jellies, and similar animals would be grouped with carnivorous plants.
below that i think the groups would be number and type of limbs, so the next groups would be quadrupedal animals, bipedal including apes, winged bipedal, and the insects and arachnids would sort based on wing shape and number/type of legs- mantises and mantisflies would be considered related, as i think they might prioritise legs over wings. crustaceans would be grouped with the arachnids. in the legless group, cetaceans and pinnipeds would get related groups, and fish would be grouped by number of fins. eels would be thought related to snakes, and legless lizards would be in that group too.
after limbs is skin/scales/fur, separatnig animals with fur, scales, feathers, just skin, exoskeletons, etc. so birds, humans, and the other primates would form three subgroups, eels and snakes would be in different groups, and lions would now be separate from elephants, but still with zebras.
next would be diet- herbivores, carnivores, insectivores, omnivores, and scavengers would now form distinct groups- i think this is self explanatory
next is distinct features each animal has down to the diet group- so parrots from finches, elephants from zebras, archerfish from guoramis, etc.
this is where i start running out of ideas… but its a start!
its also my longest post ever lol
