Okay, so the real life experience is recoil of the weapon which is the physical manifestation of Newton's third law which states that all forces between 2 objects must be in equal and opposite directions. So to propel a bullet forward, you need an equal and opposite force to be generated and that is the recoil of the weapon.
Haptic feedback is the term for touch sensation through a user interface to convey information to a user. So it could be a vibration when you hold down on a touchscreen or the rumble of a game controller to simulate recoil.
The generic term for vibration of controllers is rumble through rumble motors. Impulse triggers was kind of an Xbox One invention where you had more precision because not only were there generic rumble motors in the controller body, but you had specific rumble motors in the triggers. As far as I know, only the Xbox One has rumble triggers or impulse triggers that are fully programmable. I think they had generic rumble triggers in the past but they were either on or off and couldn't convey height and distance. But the impulse triggers had to be specifically programmed by the developer. So if a developer was doing crossplatform between PS4 and Xbox One, there was a good chance the impulse trigger would never be used since the PS4 doesn't have the feature.
And while impulse triggers add a realistic element, they put a competitive player at a disadvantage. I know a lot of competitive players try to turn off any kind of haptic feedback because anything that destabilizes a controller throws off your aim. It's like how a wheel makes a racing game more realistic but players with game controllers are often at the advantage in terms of lap times.