Potential density
Potential density is a dynamically important property: for static stability potential density must decrease upward. If it doesn't, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward; similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions (potential density decreasing upward) motion along surfaces of constant potential density (isopycnals) is energetically favored over flow across these surfaces (diapycnal flow), so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.
Specific properties
Specific properties of a substance are derived from other intrinsic and extrinsic properties (or intensive and extensive properties) of that substance. For example, the density of steel (a specific and intrinsic property) can be derived from measurements of the mass of a steel bar (an extrinsic property) divided by the volume of the bar (another extrinsic property). Similarly, the specific gravity of a liquid is derived from the density of the liquid divided by the density of water (two intrinsic properties).