if the same force is applied to a heavy object and a light object, will they move differently?
The difference between a heavy body and light body is its mass; a heavy object has more mass than a light one.
According to the second law of motion (Newton's second law), the variation experienced by the velocity of a body when subjected to a force is inversely proportional to its mass; so that, if two bodies of different masses receive the same force, the speed of the body that has less mass varies faster than the speed of the body that has greater mass.
From the expression of Newton's second law you can check this:
F = ma = m(v – v0)/t
m(v – v0) = Ft
v – v0 = Ft/m
If v0 = 0, then:
v = Ft/m
Consider that the initial rate of both bodies is zero. Then, at the same instant of time, the speed of the body with smaller mass, is greater than the speed of the body with greater mass.
So, actually, if the same force is applied to a heavy object and a light object these are going to move differently.