(foxes) are regarded sacred animals in Shintoism, being servants of the god of harvests ([]{}).

(The sign on the (Shinto archway) says .)
According to legend, a fox's favourite food is (deep-fried tofu slices). Stripes of are what makes . (By the way, can also be sliced up and filled with (sushi rice) and sesame to make .)
I'm not aware of any similar explanation for , whose characteristic ingredient is (which you might also come across as , although there is a difference between the two). My guess would be that the name was coined by analogy.