Context : Aims : To explore the role of titanium- and calcium-dust depletion in gas in and around galaxies we systematically study Ti/Ca abundance ratios in intervening absorption-line systems at low and high redshift . Methods : We investigate high-resolution optical spectra obtained by the UVES instrument at the Very Large Telescope ( VLT ) and spectroscopically analyze 34 absorption-line systems at z \leq 0.5 to measure column densities ( or limits ) for Ca ii and Ti ii . We complement our UVES data set with previously published absorption-line data on Ti/Ca for redshifts up to z \approx 3.8 . Our absorber sample contains 110 absorbers including Damped Lyman \alpha systems ( DLAs ) , sub-DLAs , and Lyman-Limit systems ( LLS ) . We compare our Ti/Ca findings with results from the Milky Way and the Magellanic Clouds and discuss the properties of Ti/Ca absorbers in the general context of quasar absorption-line systems . Results : Our analysis indicates that there are two distinct populations of absorbers with either high or low Ti/Ca ratios with a separation at \left [ \mathrm { Ti } / \mathrm { Ca } \right ] \approx 1 . While the calcium dust depletion in most of the absorbers appears to be severe , the titanium depletions are mild in systems with high Ti/Ca ratios . The derived trend indicates that absorbers with high Ti/Ca ratios have dust-to-gas ratios that are substantially lower than in the Milky Way . We characterize the overall nature of the absorbers by correlating Ti/Ca with other observables ( e.g. , metallicity , velocity-component structure ) and by modeling the ionization properties of singly-ionized Ca and Ti in different environments . Conclusions : We conclude that Ca ii and Ti ii bearing absorption-line systems trace predominantly neutral gas in the disks and inner halo regions of galaxies , where the abundance of Ca and Ti reflects the local metal and dust content of the gas . Our study suggests that the Ti/Ca ratio represents a useful measure for the gas-to-dust ratio and overall metallicity in intervening absorption-line systems .