How is motion affected by change in mass of an object and forces applied?

Newtons second law says that the acceleration of an object (produced by a net force) is directly proportional to that magnitude of the net force. E.g. F = ma
where F is the net force of an object, m is mass and a is acceleration.
For example, if an object had a large mass, there would have to be more force in order to move it than if it was lighter.  
In a linear motion, if you pushed two objects, one slightly larger than the other, with the same force, the acceleration of the smaller object would be bigger than the larger one. So the motion (change in position over time), of the larger object would be seen as lesser than the smaller one (in a situation where both forces are equal).