Actually impulse-momentum relationship is just a restated version of Newton's second law. Here's how:
Newton's second law can be resated as the change in momentum is equal to the product of the net external force and the time during which it acts: Change in momentum = Net force X Time interval.
That means a small force acting over a long time can produce the same change in momentum as a large force acting over a small period of time. The term "impulse" means the product of the force multiplied by the time over which acts, and that equals the change in momentum, according to Newton's second law. So actually Newton's second law is same as saying impulse equals change in momentum. And that is what we call the impulse-momentum relationship. Don't let people fool you with the these names again.