That is incorrect. Green Magic is a class that focuses on magic that alter statuses. There are positive effects like mentioned above, and negative effects. Wakka's section of the sphere grid contains abilities that incur various negative status effects. (Blind, Silence, Sleep)
Green Magic list can be found here.
I think of magic as broader then simply the same spell is always in the same class. For example, haste has been found in Black, White, and Time Magic classes over the course of various Final Fantasy installments.