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Column density is a measure of the amount of matter along some particular span, such as that along a line-of-sight toward a star. Specifically, it is the amount of matter per unit of area, the area being the cross-section of a tube-shape along the distance. Column mass density is mass per unit area, e.g., g/cm2 and column number density is the molecules (specifically, any particles present that the photons could react with) per unit area, e.g., cm-2. These may also be used for some specific particle type or types, e.g., electron column density, for the column number density specifically of free electrons (i.e., not counting other particles).
Column density is equivalent to surface density, each being a measure of the density through one dimension of a volume. The term surface density is generally used for measures through relatively flat volumes whereas column density is generally used for such a measurement through a volume that must traverse some significant distance. The term column density is likely to be used for the case of particles along the line-of-sight to star, whereas surface density, of particles over the course of the thickness of a disk.