When the conversation flags at the Thanksgiving table, leap in with this:
Potato came into English via the Spanish patata, a version of the word used by the Taino peoples of the Caribbean for the sweet potato, batata. The Peruvian Quechua word for the true potato of the Andes was papa. Yam comes via Portuguese from a West African word meaning “to eat.”
Source: On Food and Cooking (2004 edition), Harold McGee’s authoritative, nearly 900-page reference book.
Spanish borrowed both patata and papa; generally speaking, it’s patata in Iberian Spanish (e.g., patatas bravas) and papa in the Americas (e.g., papas a la huancaina, a traditional Peruvian dish). Take care with papa, though: when it’s capitalized it may mean “pope.”
And speaking of yams, here’s McGee on the page following the passage I cite above:
True yams are starchy tubers of tropical plants that are related to the grasses and lilies, a dozen or so cultivated species of Dioscorea from Africa, South America, and the Pacific with varying sizes, textures, colors, and flavors. They are seldom seen in mainstream American markets, where “yam” means a sugary orange sweet potato. … True yams can grow to 100 lb/50 kg and more, and in the Pacific islands have been honored with their own little houses.
P.S. McGee has nothing to say about Pilgrahoan, a virtual Mr. Potato Head-esque game sponsored by Idahoan Foods, “the industry leader in instant mashed potatoes.” Create a potato face, save the image, and receive a $1-off coupon. As for the “Pilgrahoan” name, the good news is it’ll be short-lived.