The only difference between the two pistols is the size. The .45 GAP pistol is considerably smaller than the .45 ACP, and the .45 GAP is often compared to a 9mm pistol. A smaller gun is ideal if you are trying to conceal the firearm.
Examples of this include undercover cops and secret service agents who must blend in while carrying a service firearm and being ready in case of the event that something goes wrong. The creation of the .45 GAP came to fruition because of agencies who request a more compressed form.
The bullets used in .45 GAP pistol is shorter than those in .45 ACP pistol while still preserving the equal diameter and ammunition weight. The shorter total length makes it possible to have a smaller grasp. A .45 GAP round would not fit into a .45 GAP handgun and inserting one by force and firing can cause damage to the gun.