In classical mechanics, Newton's third law states that forces occur in pairs,
one called the Action and the other the Reaction (actio et reaction in Latin).
Both forces are equal in magnitude and opposite in direction.
The distinction between action and reaction is purely arbitrary: anyone of the two forces can be considered an action,
in which case the other (corresponding) force automatically becomes its associated reaction.
The Earth orbits around the Sun because the gravitational force exerted by the Sun on the Earth (action) serves as the centripetal force that maintains the planet in the neighborhood of the Sun. Simultaneously, the Earth exerts a gravitational attraction on the Sun (reaction), which has the same amplitude as the action and an opposite direction (in this case, pulling the Sun towards the Earth).
Since the Sun's mass is very much larger than the Earth's, it does not appear to be reacting to the pull of the Earth, but in fact it does. A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass of the combined system.
Consider a mass hanging at the end of a (non-stretchable) steel cable attached to the ceiling of the laboratory. The mass is pulled towards the Earth (action) by its weight. The corresponding reaction is the gravitational force that mass exerts on the planet:
this has nothing to do with the steel cable;
in fact, the reaction exists even in the absence of the cable. On the other hand, if the tension in the cable is pulling the mass upwards and preventing it from falling, then the mass is simultaneously pulling on the cable, with equal intensity and opposite direction.
If this simple system is observed to be at rest (in particular not accelerated) with respect to the ceiling, Newton's first law implies that no net force is applied to the mass. Since we have just seen that two distinct forces do apply to the mass (the gravitational pull from the Earth and the tension from the cable), we conclude that these two forces are themselves equal and opposite,
i.e.,
that they compensate each other. However, these latter two forces are not the action and the reaction of each other.
To verify the correct interpretation of these concepts, let's replace the cable by a spring, and consider the same system initially at rest (again with respect to the ceiling of the laboratory):
The same considerations apply.
However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's first law that a net force is responsible for the observed change in velocity.
Yet, the gravitational action and reaction remain the same, since the masses involved have not changed, and the distance between the center of mass of the object and the center of mass of the Earth is modified so slightly that any variation in the gravitational force is immeasurably small.
What has occurred is that we now have a dynamic system where the (constant) gravitational force on the mass is temporarily out of balance with the (variable) tension in the spring. The latter changes intensity and direction in time (at a frequency that is related to the strength of the spring),
depending (in first approximation, and for small perturbations) on the deviation of the length of the spring with respect to its 'natural' length
(i.e., in the absence of a mass).
In classical mechanics the term ground reaction force (GRF) refers generically to any force exerted by the ground on a body in contact with it.
For example, a person standing on the ground exerts a force on it (equal to the person's weight) and at the same time an equal and opposite ground reaction force is exerted by the ground on the person.
The use of the word reaction derives from Newton's third law, which essentially states that if a force, called action, acts upon a body, then an equal and opposite force, called reaction, must act upon another body.
The force exerted by the ground is commonly referred to as the reaction, although the distinction between action and reaction is completely arbitrary and the expression ground action would be in principle equally acceptable.