According to Newton’s Theory of Gravity, every single object in the universe attracts every other object in the universe with a force which vary directly to the product of masses of the two bodies and this force vary inversely to the square of distance between them.
This means that larger the masses of the two objects (or single), larger the force of gravity and larger the distance between the two objects, smaller the force.
On the other hand, Einstein’s General Theory of Relativity is the currently accepted model of Gravity which describes gravity as follows:
Gravity is not a force like other, but, it is a consequence of curvature of space-time.
The presence of mass and energy curves space-time that means near a mass, space contracts and time dilates and away from the mass, space is less contracted and time is less dilated. This ‘gravitational contraction of space and dilation of time’ is known as ‘distortion of space-time’ or ‘curvature of space-time’.
And because, space is contracted, it pushes all the objects in its path. This actually causes gravitational effects.
And, space pushes the objects in straight paths in 4-dimensional space-time but the objects may seem to move in curved paths in 3-dimensional space.
In brief, the difference can be understood by the infographic below: