Gulf, chasm, abysm, abyss basically denote a hollow place of vast width and depth in the earth.
Gulf and chasm suggest a depth which, though vast, is still measurable; abysm and abyss suggest immeasurable depth.
Gulf is the most general term and may properly be used of any wide and deep hollow place. In its extended use gulf suggests separation by a great, often unbridgeable distance.
Chasm adds the implication of a deep and sometimes wide breach in a formerly solid surface. In extended use chasm still stresses a sharp break in continuity. Abysm and abyss may designate the bottomless gulf or cavity of ancient cosmogonies and both have been applied to hell when thought of as a bottomless pit; in other applications they usually connote not only fathomlessness but also darkness and horror.
Abysm is somewhat old-fashioned.
Abyss is commoner in general modern use and, like abysm, it carries over into its extended uses the notion of vast, immeasurable void.