So, the images you use to represent your Carnifex are kind of like pictures of different breeds of dogs. Astounding diversity, but they're all the same species.
... which leads to this thought: the existence of half-elves and half-orcs demonstrates that elves and orcs are one species with humans, much as earlier modern humans crossbred with Denisovians and Neandertals.
[For the sake of this commentary, let's ignore the fact that all the races except humans in D&D are the product of intelligent design by gods created by the writers, not of evolution.]
Hmmm.
Is it possible that orcs and elves can also produce viable orc-elf offspring? Do they refrain from it simply because of mutual antipathy, or have each of their races, while still fecundable (a new word, or a grammatical travesty!?) with humans, evolved far enough away from each other to be genetically separate species from each other?
I'm starting to think that D&D might spawn its own school of taxonomy, insofar as our collective creativity is leading to greater diversity in our imagined life forms, and the problems arising from too many choices.
The term "humanoid", referring generally to bipedal creatures, has its mammalian group (humans, elves, orcs, dwarves, etc.), its reptilian group (dragonborn, lizardfolk, kobolds, some yuan-ti, etc.), and plant-based (myconids, treants, wilden).
The tauric, or sagittarean, lines muck it up a bit, putting a humanoid torso onto a quadrupedal base. The DM's Guild published Tauric Races, which groups them into mammals, reptiles, insects (thri-kreen and tosculi are the two types I'm aware of - the latter is a distinct offering from 13th Age/Midgard for 5e), and snakes (the other yuan-tis, and nagas, I guess).
Since I like creating at least one PC with each possible combination of race and class, I'm now looking at the need for about an extra 132 years of life to get it done. I'm delusional enough to be okay with that, because I think I'm a gnome.