There are only two choices when it comes to shotguns in Call of Duty 4. There is the MOG 12, which is a higher damage pump action shotgun, and the SG12 which is a lower damage and range but semi-automatic shotgun. Both are not easy to use and require you to move around the map so that you don’t encounter enemies at medium or long range. Even then you often need multiple shots to secure a kill.
The MOG 12 has better range and damage. It is best if you are accurate and shots can be followed up by melee which is often enough to confirm that kill.
However, the SG12 is much easier to use than the MOG 12 as it is semi automatic and fires more pallets per shot making it more reliable. It has several good attachments available that help out with its lower damage and range. Therefore, overall, the SG12 is the best shotgun in Call of Duty Black Ops 4.