There are two main species of the genus Zea (out of six total): Zea mays - common corn and Zea diploperennsis - teosinte (a perennial wild variety), which is more of a weed that readily crosses with corn.
An annual variety of teosinte (teosynta) called Zea mays mexicana is the closest botanical relative of corn. It still grows in the wild as an annual plant in Mexico and Guatemala.
Maize is believed to be a degenerate form of this grass that evolved through mutation and was perpetuated by humans.