One way to characterize and understand H I-selected galaxies is to study their metallicity properties. In particular, we show that the metallicity of absorbers is a bivariate function of the H I column density (N H I ) and the Mg II equivalent width (W λ2796 r ). Thus, a selection upon W λ2796 r is not equivalent to a H I selection for intervening absorbers. A direct consequence for damped absorbers with log N H I > 20.3 that falls from the bivariate metallicity distribution is that any correlation between the metallicity [X/H] and velocity width (using W λ2796 r as a proxy) cannot be interpreted as a signature of the mass-metallicity relation akin to normal field galaxies. In other words, damped Lyα absorber (DLA) samples are intrinsically heterogeneous and the [X/H]-W λ2796 r or [X/H]v correlation reported in the literature arises from the H I cut. On the other hand, a sample of Mg II-selected absorbers, which are statistically dominated by lowest N H I systems (sub-DLAs) at each W λ2796 r , is found to have a more uniform metallicity distribution. We postulate that the bivariate distribution [[X/H](N H I , W λ2796 r )] can be explained by two different physical origins of absorbers, namely sight lines through the interstellar medium of small galaxies and sight lines through the out-flowing material. Several published results follow from the bivariate [X/H] distribution, namely (i) the properties of the two classes of DLAs, reported by Wolfe et al. and (ii) the constant dust-to-gas ratio for Mg II absorbers.