Corn comes from Mexico and was believed to be cultivated starting around 8,000 BC. So it seems odd that the Japanese word for corn is not a loanword from English or Spanish but the interesting word tōmorokoshi. The Japanese thought that corn greatly resembled sorghum, so they called it tō- (foreign) morokoshi (sorghum, or millet).
Potatoes are originally from South America, but were introduced to Japan via Indonesia. The Japanese word for potato (jagaimo) comes from the words jaga- which is short for Jakarta, and -imo, which means root.