Yes, IRL Shingon Buddhism. The Ise Grand shrine where Amaterasu is enshrined went through a lot of crazy shit back then and finally they syncretized Amaterasu with Dakini-ten and Inari, then Kukai (founder of Shingon Buddhism) decided that Amaterasu is the highest manifestation of Dainichi Nyorai (Vairocana Buddha). And Dakini-ten is the nine tailed fox, aka Tamamo. There's even more connections through Taira no Kiyomori's myth. According to the myth he met a nine tailed fox one day while traveling, who revealed itself to be the Dakini-ten. This fox granted him immsense evil power to oppose the Minamoto clan and the government set up under Ex-Emperor Toba (notice this familiar name?) which later exploded into the legendary Genpei war between the Taira and Minamoto clan many years later. Some said Kiyomori used the curses he got from the fox to curse Toba (Tamamo cursed Toba).
That is because in Shingon Buddhism, Dainichi Nyorai (Vairocana) is the ultimate Buddha, the Root, the equivalent to YHVH, while Gautama Buddha (Saver) is just one of the many other Buddhas manifested from Dainichi. That's why his NP is actually the ring of authority originally behind Dainichi Nyorai and his NP name is referencing Amida - the Mahayana's equivalent to Dainichi.
Of course I'm salty because I'm Theravada Buddhist where Gautama is really really important. But what can I do about Japan and Nasu's love for Kukai?
Yes.
I'm not gonna diss you due to your lack of knowledge of the matter, this is a common question I've seen not just here but other places (read: reddit).
http://yokai.com/tamamonomae/
That + the stuffs I said above.