Typically, firing one-handed was the classic way to fire most guns of handgun size, and still is for those like revolvers, which don't really work as well two-handed because the recoil is an important part of the firing pattern and using one arm while using one's arm to direct the recoil is an important part of using a revolver. The two-handed stance, also called the Weaver stance, is more modern and is generally used to help keep most pistols steady while aiming, especially the heavier varieties that can drag down the arm, with the off hand used to steady the gun by the grip while the other pulls the trigger.
It's entirely possible to fire almost any gun above handgun or light SMG one handed, but accuracy will go down extremely due to recoil, the extra weight of the weapon, and the lack of steadiness afforded by two hands, unless one has the arms of a gorilla.