If you want a really weeaboo try-hard explanation:
Yumeiko is more like a kenzoku, a fox spirit contracted to serve Inari no Okami as a servant.
Miyuki, on the other hand, is more akin to a traditional youkai, an actual "monster" who messes with humans.
Miyuki has no ties or connections to any gods or goddesses and doesn't practice any religions, unlike Yumeiko. She may aid or assist the latter with her worship, from time to time, but she doesn't do any actual praying or other faith-based actions of her own accord.
Oh, and yes, they're both fox spirits but they're different kinds. Kinda like how a brown bear and a panda are both bears, but different species.
Yumeiko is more like a kenzoku, a fox spirit contracted to serve Inari no Okami as a servant.
Miyuki, on the other hand, is more akin to a traditional youkai, an actual "monster" who messes with humans.
Miyuki has no ties or connections to any gods or goddesses and doesn't practice any religions, unlike Yumeiko. She may aid or assist the latter with her worship, from time to time, but she doesn't do any actual praying or other faith-based actions of her own accord.
EDIT:
Oh, and yes, they're both fox spirits but they're different kinds. Kinda like how a brown bear and a panda are both bears, but different species.