Give it another read. The F=ma example is the simplified state to which perturbations are applied; like the example of the simplified (traditional) model of the atom to which perturbations are applied because the simplified model does not represent reality.

Tom Bishop, that Wikipedia article says "Typically, the 'conditions' that represent reality are a formula (or several) that specifically express some physical law, like Newton's second law, the force-acceleration equation, F=ma.". In that sentence, I interpret "conditions that represent reality" to mean that F=ma can describe reality rather than only a simplification of it. Do you believe that Wikipedia is saying that F=ma can only be "the simplified state"? Can you explain in more detail why you interpret Wikipedia to be saying that? (I'm not sure what you mean when you refer to an equation as a "state". In physics literature that I have read the "state" is usually the information about the physical system: positions and velocities of the orbiting bodies in this example.)

Of course F=ma can describe a simplified model when some forces are not included in F. For example, in the full model describing the Moon's motion, F could include all gravitational forces from the Sun, Earth, Mars, Venus, asteroids, and all other objects acting on the Moon. In that case F=ma would represent reality, but the exact orbit would be difficult to calculate, so one might temporarily neglect smaller forces. An approximate orbital path can be calculated using only the force caused by the Earth acting on the Moon. Then a better approximation can be obtained by including effects of the forces that were neglected. That process of obtaining a better approximation is what we call "perturbation".