We consider the questions of whether the damped Lyman-alpha (DLA) and sub-DLA absorbers in quasar spectra differ intrinsically in metallicity, and whether they could arise in galaxies of different masses. Using the recent measurements of the robust metallicity indicators Zn and S in DLAs and sub-DLAs, we confirm that sub-DLAs have higher mean metallicities than DLAs, especially at $z lesssim 2$. We find that the intercept of the metallicity-redshift relation derived from Zn and S is higher than that derived from Fe by 0.5-0.6 dex. We also show that, while there is a correlation between the metallicity and the rest equivalent width of Mg II $lambda 2796$ or Fe II $lambda 2599$ for DLAs, no correlation is seen for sub-DLAs. Given this, and the similar Mg II or Fe II selection criteria employed in the discovery of both types of systems at lower redshifts, the difference between metallicities of DLAs and sub-DLAs appears to be real and not an artefact of selection. This conclusion is supported by our simulations of Mg II $lambda 2796$ and Fe II $lambda 2599$ lines for a wide range of physical conditions. On examining the velocity spreads of the absorbers, we find that sub-DLAs show somewhat higher mean and median velocity spreads ($Delta v$), and an excess of systems with $Delta v > 150$ km s$^{-1}$, than DLAs. Compared to DLAs, the [Mn/Fe] vs. [Zn/H] trend for sub-DLAs appears to be steeper and closer to the trend for Galactic bulge and thick disk stars, possibly suggesting different stellar populations. The absorber data appear to be consistent with galaxy down-sizing. The data are also consistent with the relative number densities of low-mass and high-mass galaxies. It is thus plausible that sub-DLAs arise in more massive galaxies on average than DLAs.
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