AddForce applies force, which means that a new force will be pushing the body in given direction (ie body keeps accelerating as if constantly being pushed, as described by Newton).
AddImpulse applies force during one time instance. It is something like hitting the body and then leaving alone (ie no further acceleration is applied).
In short:
AddForce - employ someone who will push the body constantly
AddImpluse - kick the body

You can also get AddForce effect by repeatedly calling AddImpulse.