What is Difference between Acceleration due to Gravity and Gravitational Field Intensity?
The two quantities are on opposite sides of Newton's second law equation $\vec F=m\,\vec a$
The force on a mass $m$ in a gravitation field $\vec g (= g \,\hat d)$ is $\vec F = m \,\vec g = m\, g\,\hat d$ where $g$ is the magnitude of the gravitational field strength and $\hat d$ is the unit vector in the down direction.
Assuming no air resistance then using this force and Newton's second law you can find the acceleration of the mass in free fall.
$\vec F =m\, \vec a \Rightarrow m\, g\,\hat d = m\,\vec a = m\,a\, \hat d \Rightarrow \vec a = a \,\hat d = g \,\hat d$ where $a$ is the magnitude of the acceleration.
So the acceleration of free fall $\vec a$ has the same magnitude as the gravitational field strength $g$ and is in the same direction $\hat d$.
To differentiate between the two quantities you can use $\rm N\, kg^{-1}$ as the unit of gravitational field strength and $\rm m\, s^{-2}$ as the unit of acceleration although dimensionally they are the same.
Gravitational Intensity and Gravitation acceleration , even though have same dimensions are different physical quantities.
Gravitational Intensity of a mass body A at a given point is defined as the force on a unit mass body. It is just a physical quantity that is defined to help us find out the force exerted by the mass body A on any given mass in its field. So, if at any particular instant the gravitational intensity at a given is E , it does not imply that the gravitational acceleration of any mass at that point is equal to E, it's gravitational acceleration corresponds to the resultant force on it due to other bodies . For eg. Consider Moon, to find out the force exerted by the sun on it, we find out the gravitational intensity of the Sun at that point , but that does not mean that it is the gravitational acceleration.
Even for an isolated system of two bodies, gravitational intensity at a point is the property of the gravitational field associated with the mass A in consideration above, while the gravitational acceleration is the property of the other mass which is present in mass A 's gravitational field, that is even if the other body isn't present, gravitational intensity will be defined whereas gravitational acceleration will not be.