I don't know how DF does it, but as far as I know all fortress members are placed in one of the Units, Animals, or Dead tabs (the names may be off, and the Dead one also adds dead non fortress members).



I'd expect a unit to show up in either of the Units or Animals tabs if it belongs to the fortress and isn't dead (ghosts are not dead in this regard, they're just not alive).

Beyond that, I expect units to end up in the Animals tab if they're marked as Trained at any level above wild. Note that this causes Gremlins to end up on the Animal tab (as well as on the animals stock screen, where they can be marked for butchering).

However, I (and I'd expect others who engage in training sapients) definitely prefer DT to allow you to control your intelligent "pets" as normal citizens, which means that intelligence would override training.

Caged creatures that are not tamed (i.e. fully wild, which includes "normal" sapients such as gobbos) show up on the Others unit tab and move after training, but trainable animals show up on the Animals stock screen (which is reasonable, as that's where you order them to be trained if you don't do that directly on the unit itself [and I don't think you can reach that option if it's caged]). I'd expect chained animals to behave the same as caged, but I rarely use chains. I don't think there are any further options beyond cages and chains to have wild animals under control, and I don't know how they're displayed while in transit between one cage/chain and another (a period during which they can potentially break free).



Much guesswork above...



Edit:

I think the tags controlling HOW creatures can become tame are irrelevant to how DF treats them once they are tamed (to some level).