Satoimo vs. Taro vs. Yam (Yamaimo)
While Taro or 太郎 in Japanese is a common name for males in Japan, the one in English refers to a tropical plant grown for its edible corms in Asian cultures.
According to the article Taro in English Wikipedia, the root vegetable has the botanical name Colocasia esculenta.
It is a species in the genus Colocasia that belongs to the family Araceae, commonly known in Japan as Satoimo (サトイモ/里芋).
Satoimo vs. Taro vs. Yamaimo Yam
As you can see in the article サトイモ on Japanese Wikipedia, the botanical name of Satoimo is also Colocasia esculenta, which manifests Taro and Satoimo are the same things.
The Satoimo taro is similar to the Japanese yam Yamaimo (山芋), but the latter has the botanical name Dioscorea japonica, which belongs to the family Dioscoreaceae.
In the names Yamaimo and Satoimo, Yama (山: meaning mountain) and Sato (里: village or town) denote where the plants grow, while Imo generally means potato in Japanese.
The Japanese yam, Yamaimo, is viscous compared to Satoimo taro, and the grated one is generally called Tororo (とろろ).
Tororo on Tuna Sashimi
The Tororo yam paste/liquid is used in various Japanese dishes and can be a thickener for Soba buckwheat noodles or Okonomiyaki pancake.
In contrast, Satoimo is usually not grated but simmered (after being cut into bite-size pieces) and eaten in Nimono form or soups.
Satoimo in Inakani (田舎煮)