corn (n.1) Look up corn at Dictionary.com
"grain," Old English corn, from Proto-Germanic *kurnam "small seed" (source also of Old Frisian and Old Saxon korn "grain," Middle Dutch coren, German Korn, Old Norse korn, Gothic kaurn), from PIE root *gre-no- "grain" (source also of Old Church Slavonic zruno "grain," Latin granum "seed," Lithuanian žirnis "pea"). The sense of the Old English word was "grain with the seed still in" (as in barleycorn) rather than a particular plant.

Locally understood to denote the leading crop of a district. Restricted to the indigenous "maize" in America (c. 1600, originally Indian corn, but the adjective was dropped), usually wheat in England, oats in Scotland and Ireland, while Korn means "rye" in parts of Germany. Maize was introduced to China by 1550, it thrived where rice did not grow well and was a significant factor in the 18th century population boom there. Cornflakes first recorded 1907. Corned beef so called for the "corns" or grains of salt with which it is preserved; from verb corn "to salt" (1560s).
corn (n.2) Look up corn at Dictionary.com
"hardening of skin," early 15c., from Old French corne (13c.) "horn (of an animal)," later, "corn on the foot," from Latin cornu "horn," from PIE *ker- (1) "horn; head, uppermost part of the body" (see horn (n.)).