I have read that gravitational field intensity and acceleration due to gravity are two different physical quantities that have the same direction, magnitude, and units. So, if all the units, magnitudes, and directions are the same for the two quantities (and also, physically, both essentially mean the acceleration produced in a point mass at a point) then what is the difference between them?
As a couple of answers point out, physically, the two quantities are different as the former (the field intensity) is the quantity that describes the physical entity that the gravitational field is at a certain point whereas the latter (the acceleration due to gravity) describes the acceleration (a characteristic of the motion) of the particle put in the field. The answer by @jaydesai10 makes this difference rather transparent via pointing out that the field intensity will always be present at a point (as long as the source of the gravitational field is around) but the acceleration due to gravity will be relevant only when an actual particle is put in the field to experience the field.
I would like to point out that the curious fact that these two (meant to be different) quantities generically turn out to be the same in their values is thus a non-trivial fact--in other words, a law of nature. The popular name for this law is, of course, the (weak) equivalence principle. The fact that this is, in fact, non-trivial can be seen via comparing the situation to the situation in electrostatics where the electric field intensity at a point and the acceleration produced (due to the electric field) in a charged particle put at that point are clearly two different quantities. The relation between these two quantities depends on the ratio of the electric charge and the inertial mass of the particle in question. And this ratio, as we know, turns out to be different for different particles--unlike the gravitational scenario where the ratio of the gravitational mass and the inertial mass is independent of the particle in question (which is essentially the statement of the weak equivalence principle).