I am not able to reconcile what D&D really means by "race", other than the tables of abilities in the player's handbook.
The basic biological taxonomy goes as follows: kingdom, phylum, class, order, family, genus, and species
Then where do Tieflings branch away from humans? They seem to have a spinal cord, so the phylum "chordata" is the same. I would guess they could be considered mammals? But on the other hand, maybe they could actually be in a different class. Once again, the virtue of unknowing reveals itself.
The taxonomical classifications in Faerun do not reflect real life.
They are:
Humanoids: Any human-sized and vaguely human-shaped race. Beasts: Non-sapient but naturally created creatures. Aberrations: Tentacly creatures with crazy mind powers that usually come from other worlds. Fey: Creatures from the Feywild. Elemental: Elemental beings from the Elemental Planes. Monstrosities: Usually magically created or otherwise freakish mutant things. Fiends: Denizens of the lower planes. Celestials: Denizens of the upper planes. Dragons: Draconic creatures like dragons, wyverns, etc. For some reason kobolds and dragonborn don't count.
Probably more than I am missing.
Humans, gnomes, elves, etc are all humanoids. So are tabaxi, lizardfolk, tieflings, dragonborn, etc.
Some humanoids have ancestry that could classify then as something else but don't for mostly mechanical reasons. Dragonborn and kobolds are humanoids that are related to dragons. Tieflings are humanoids who are related to fiends. Shoot, elves are humanoids related to the Fey.
The concept of species is mostly meaningless in Faerun. Some races can breed true like humans, orcs, and elves while others cannot (to the best of my knowledge, I could be wrong) like dragonborn and lizardfolk. And even then with magic all things are possible. Dragons can breed true with basically anything with the use of polymorph.
Tieflings are the descendents of humans who made some blood pacts with devils for power. Thus the tieflings look like devils due to what their ancestors did but aren't actually bound to the Hells in any way, meaning they can be just as good or evil as anyone else.
On the other hand Yuan-Ti were humans who decided snakes were rad and went through some crazy rituals to become snake people. Part of this ritual involved killing their empathy for others, which is why their race is uniformly evil.
Both are new races that spun off from humanity due to magic shenanigans but their capacity for good is very different.
