The cotton plant is commonly referred to as Gossypium, which is its genus name, and it has several species within that genus. The most widely cultivated species is Gossypium hirsutum, which is the upland cotton, and then there's Gossypium barbadense, known as extra-long staple cotton or Egyptian cotton. Sometimes you might see it just called cotton or cotton plant, but technically speaking, Gossypium is the correct term to use when referring to the plant itself, and the different species names are used to specify the type of cotton being referred to.
