Hmm... for me it's like, hard to explain? Especially between my wolf and leopard theriotypes, because I'm constantly mentally both of them to some degree (which is why it took me so long to distinguish the leopard parts from the wolf parts - it all mushes together in my head). I'll get feelings and instincts from both species, but the basic feeling associated with them is the same; there's no clearly "wolf instincts" or "leopard instincts", but I can figure out where a particular instinct is coming from with a little logic. Wanting to run with a pack is clearly a wolf thing, while wanting to stalk and ambush is more of a leopard thing. Wanting to hiss at cats I see around is certainly a leopard thing, whereas my wolf instincts are either "ignore the cat" or "oh look it's a weird puppy, new friend!" depending on my mood. :Raspberry:
I don't get astral shifts, I don't think, but my phantom shifts have a similar level of fluidity and "mushiness" to my mental ones - I always have wolf ears, but I might use those ears in a feline way sometimes. Or I might have wolf ears and a leopard tail. Or a wolf face but leopard paws. It doesn't feel weird to me. Both theriotypes are equally me, and I'm one person, so my theriotypes are both the same me... just. In different ways, I suppose? It's hard to explain.
It's funny, I remember when I only knew about my wolf theriotype and didn't understand how anyone could be more than one thing! Welp, turns out the answer, for me, is that I'm not "more than one thing". I'm just three completely different things mushed and tangled together, with no clear division between them.