The name “yam” is used for a few different root vegetables.
The word is from West Africa and refers originally to Dioscorea yams, which are found in many parts of the world — having been independently domesticated in Africa, Asia, and the Americas. The word “yam” is related to the Fulani word for “to eat”, and was introduced into European languages by way of Portuguese colonizers.
But in the US, “yam” almost always refers to a variety of sweet-potato (Ipomoea genus), which is more closely related to a morning-glory flower than to either Dioscorea or a true potato (which is a Solanum nightshade).
Both sweet-potatoes and potatoes are native to the Americas. Sweet-potatoes probably were grown first in the Yucatán or in eastern South America, while true potatoes are from Peru and western South America.
Meanwhile in New Zealand, a “yam” is oca, an Oxalis species — close relatives of sourgrass and redwood sorrel. And in Malaysia, “yam” is taro root!