All can be found at the Mexican grocery store. Is there a difference in the way the plant looks when you grow it? Will all of them grow?
Taro is generally Colocasia esculenta which has 100's of forms. Common names: Giant Elephant Ear, Elephant Ear, Black Magic, Taro, Wild Taro, Dasheen, Dachine, Black Taro, Dalo, Eddo, Eddoe, Edda, Eddy Root, Green Taro,
Coco Yam, Kalo, Callaloo, Poi, Katchu, Potato of the Tropics, and in Ecuador: Papachina. The common name depends on the culture.
Malanga is normally Xanthosoma.sagittifolium (L.) Schott, common names Arrowleaf "Elephant Ear", Malanga, Yautia, Tannia, MangarÃ¡s, New Cocoyam, Tajer, Tanier, Taioba, Chou Caribe, Cascamote and many other common names depending on the country.
All should grow from the tuber you can buy in groceries.
Yucca is not an aroid.
Here is a link that might be useful: Colocasia esculenta