Gravitational Acceleration vs Gravitational Constant

Gravitational acceleration and the gravitational constant are two fundamental concepts in physics related to gravity, but they refer to different aspects.

Gravitational Acceleration

Definition  -  Gravitational acceleration is the acceleration experienced by an object due to the gravitational pull of a massive body like the Earth.
Symbol: g
Value  -  On Earth's surface, the standard value of is approximately  \(g = 9.80665 \;\;m / s^2\) (Metric)  and  \(g = 32.1740 \;\; ft / sec^2\) (English)
Variation  -  The value of g can vary slightly depending on altitude, latitude, and local geological structures.  It decreases with altitude and varies with the distribution of mass within the Earth.
Formula  -  For an object near the surface of the Earth,  \( g = (G \; m) \;/\; r^2 \)​

Gravitational Constant

Definition  -  The gravitational constant is a fundamental constant of nature that appears in Newton's law of universal gravitation.
Symbol  -  G
Value  -   In the correct units, the gravitational constant is exactly 1!  The value of G is approximately  \(G = 6.67408 \;10^{-11} \;\; N-m^2 / kg^2 \) (Metric)  and  \(3.333 \;10^{-10} \;\;lbf-ft^2 / lbm^2\) (English)
Usage  -  G is used to calculate the gravitational force between two masses.
Formula  -  Newton's law of universal gravitation is given by  \( F_g  = G \; ( m_1 \; m_2 \;/\; r^2 ) \)              

Key Differences

Nature  -  Gravitational acceleration g is a measure of the effect of gravity on an object, specifically the acceleration it experiences.  The gravitational constant G is a universal constant that quantifies the strength of the gravitational force.
Units  -  g is measured in \(m / s^2\), while G is measured  \( N-m^2 / kg^2 \) .
Dependence  -  The value of g depends on the mass and radius of the Earth (or other celestial body), whereas G is a fixed constant that applies universally to all masses.

To summary, g describes the specific gravitational pull at a point near a massive object like Earth, while G is a fundamental constant that applies to the gravitational interaction between any two masses.