In Japanese, there are several terms used for aburaage, or deep-fried tofu. The general term is aburaage (油揚げ), but when used in inari sushi, it's called inari (稲荷), and when served on udon or soba, it's referred to as kitsune (きつね).
Aburaage is traditionally offered to the deity Inari at Inari shrines, which is why it’s called inari in inari sushi.
So why is the tofu on udon called kitsune? Kitsune means “fox,” and at Inari shrines, offerings are also made to foxes, who are considered the messengers of Inari. Foxes were seen as helpful protectors of rice fields by eating mice. That’s why the fried tofu on noodles is affectionately called kitsune.