What is the difference between an application of an impulse and an application of a force in relation to a physics engine?
An impulse is applied instantly, so it does not depend on the time step. You would use an impulse when you want to give a fixed boost of speed to something, or the physical action happens too quickly (ex. bullets/gun ricochet, collisions, jumps, instant speed ups).
Meanwhile a force changes the speed directly proportional to the time step. You use it for things that have an over time effect (ex. gravity, long springs, air resistance).
If you expand the first, you can check this: