Force of Gravity:
The force of gravity refers to the attractive force that exists between any two objects with mass. It is the force that pulls objects towards each other and is responsible for the phenomenon of weight. The force of gravity is always present, and its magnitude depends on the masses of the objects involved and the distance between them.

Gravitational Force:
Gravitational force, on the other hand, is a more general term that encompasses all the forces associated with gravity. It includes not only the force of gravity between two objects but also the gravitational forces exerted by larger celestial bodies, such as planets, stars, and galaxies.

Differences:

1. Scope:
- The force of gravity specifically refers to the attractive force between two objects with mass.
- Gravitational force, on the other hand, includes the force of gravity as well as other gravitational forces exerted by larger celestial bodies.

2. Magnitude:
- The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, according to Newton's law of universal gravitation.
- Gravitational forces exerted by larger celestial bodies, such as planets or stars, are influenced by their mass and distance but also by other factors such as their size and composition.

3. Effect:
- The force of gravity between two objects determines their weight. It is responsible for keeping objects grounded on the Earth's surface and is essential for the functioning of many natural phenomena, such as tides.
- Gravitational forces exerted by larger celestial bodies have a wide range of effects, including the orbits of planets around the sun, the formation of galaxies, and the overall structure of the universe.

4. Interaction:
- The force of gravity between two objects is a mutual force, meaning it acts on both objects equally and in opposite directions. For example, the Earth pulls an object towards its center, while the object pulls the Earth with an equal magnitude but in the opposite direction.
- Gravitational forces exerted by larger celestial bodies also follow the same principle, where both objects or bodies exert a force on each other.

In summary, the force of gravity specifically refers to the attractive force between two objects with mass, while gravitational force is a broader term that encompasses all the forces associated with gravity. The force of gravity determines an object's weight and is responsible for keeping objects grounded, while gravitational forces exerted by larger celestial bodies have a wide range of effects on celestial phenomena. The force of gravity acts mutually on two objects, while gravitational forces between larger celestial bodies also follow the same principle.