I think what distinguishes supernatural/eldritch horror from cosmic horror is that the latter isn’t just big and old and from far away, its existence forces the protagonists to reevaluate what it means to be human.
Unicron from The Transformers: The Movie is eldritch but not cosmic, because even though he’s huge and from outer space, he’s a familiar archetype: a mix of Satan, Apep, and Ahriman.
By contrast, the extraterrestrials in Blindsight are somehow highly intelligent despite not being sentient, the powerful artifacts that alter our understanding of science in Roadside Picnic are worthless litter to the visitors that left them, and “At The Mountains of Madness” introduces the idea that humankind is the descendant of the mold that grew in some primordial race’s fridge, something Ringworld/Known Space, Xenogears, Crysis, etc. all play with.
