In theory, your off road tuned shocks have less damping for slow speed compression/rebound and then an aggressive high speed damping in rebound and compression. They are also often one size larger diameter.
The idea being it allows tires to remain in contact with terrain off road i.e. rock crawling at extreme, while preventing suspension from bottoming out on bump stops while traveling over whoops at speed. The larger diameter decreases fade when running over uneven terrain.
It does have some negatives during on road driving - during cornering/braking the vehicle will tend to move more - roll/dive respectively. And ride over potholes*/expansion joints will tend to be rougher as you aren't getting as much suspension travel.
For OEMs, the differences will be minor. For the racing crowd, you can make some serious tuning changes with the high end shocks (up to 8 different bypass valves). There is a reason the Fox shocks on the Raptor cost ~10X what the stock ones do. It isn't all brand name.
*Assumes pothole wasn't so deep that the suspension max'd out. Things get really rough if you hit bump stops.