Before I begin, let me point out that I am no expert in Folklore, and that I may be working under one or more pieces of bad information. As such, I would welcome constructive corrections.
As I understand it, Fae are a broad grouping of Spirits, mostly of nature and natural phenomenon, but occasionally of unnatural ones as well; Brownies being spirits of Hearth and Home, while Redcaps are spirits of Blood and Murder. While a few are helpful, and some are malevolent, for the most part they are mischievous and alien. They tend to be prone to taking insult for things that make little sense to Mortal Men, and will not forgive an insult during a man's lifetime. It is best for men to avoid their notice, and if you gain their notice, to be very polite and hope to escape their attention.
Also as I understand it, Yokai are also a broad group of spirits, often of nature or natural phenomenon, but also spirits of man that have not passed on to the afterlife and animals that have grown beyond the limits of natural creatures. While they can be helpful or vile as individuals, as a group of species they tend towards being mischievous or alien rather then good or evil. Mind you, this includes spirits like the Yuki-Onna that live in the coldest of places and are drawn to the heat of men's bodies, taking it to warm themselves or the Jorogumo that views humanity as a convenient protein source, but this is an alien mindset, not an evil one; after all, a wolf is not evil just because it might eat a man. Compare to Yoma, which are universally evil, demonic spirits....
Like with the Fae, the best recourse with Yokai is to avoid their notice, and to be exceedingly polite if you gain it. Also like with the Fae, tales of Yokai tend to be cautionary, with the near universal take away being to stay the hell away from them. This is why I tend to view them as being functionally the same in nature, differing in details as the products of very different cultures but serving the same purpose in the folklore of their respective cultures. Or at least, that's my personal view......
Now, to a point more in line with this specific story, I would note a five tailed fox spirit may not be exclusively Japanese in origins, but is definitely a product of East Asian folklore. I would also note that a Drider may be the product of High Fantasy, but in terms of folklore they most resemble a Jorogumo's natural form in appearance. Does this mean the ABB might be looking to press-gang Lisa and Dinah into their ranks as such obviously Asian supernatural creatures? After all, with Lung in captivity, they would definitely be hurting for parahuman support, and Bakuda has a history of conscripting new members for the gang.....