Eh, human Tamamo.
I just mean this as a fun observation, but wow man, your far-stretched mythological connections make it seem like you wrote for the Campione light novels.
This is not far fetched.
Basically, in Fate Extra CCC, we get to meet "
Amaterasu gone delinquent".
However, the spirit that we meet is not labelled as "Amaterasu", rather, it is called "Golden White Face".
This is the very name that one uses to identify the 'disaster' that went from China to India to Japan. A group of Meiji Folklorists did an analysis of the legends and related this to Hokusai's information, found
here.
Nasu himself has stated that Tamamo is not a Fox Spirit, but should more properly be called a Dakini-type. She uses witchcraft too (but opts not to in the game), techniques of Deva, which do not originate from Japan but find their roots in Buddhism. It's in the backstory of Tamamo herself -- I went to replay F/E and note down Tamamo's Dialogue, also, went up to check CCC's translations for this project.
Now, as to how they can be different embodiments. When the protagonist comes out of the vision of 'Golden White Faced', Tamamo tells them to 'forget what they've seen'. It is because she is deeply hateful of her 'past self', which she identifies as a different existence.
That 'past-self' is Daji.
Now, how can Daji and Tamamo No Mae be different if even in Nasu Canon, they're stated to be all aspects of Amaterasu, and according to legends (which Nasu correlates), it was the same Spirit that wrecked all of this Chaos?
Simple. In Daji's tale, it was said that Daji was originally a normal woman, however, the Spirit that took hold of her ate her soul and became one with her. A level above possession.
The same could be said for Misukume, who was potentially a human being at first, but them, the Spirit merged with Misukume and gave birth to Tamamo No Mae.
While it is the same spirit everywhere, the 'vessel' used is different.
