We present the second and final release of optical spectroscopy of Type Ia supernovae (SNe Ia) obtained during the first and second phases of the Carnegie Supernova Project (CSP-I and CSP-II). The newly released data consist of 148 spectra of 30 SNe Ia observed in the course of CSP-I and 234 spectra of 127 SNe Ia obtained during CSP-II. We also present 216 optical spectra of 46 historical SNe Ia, including 53 spectra of 30 SNe Ia observed by the Calán/Tololo Supernova Survey. We combine these observations with previously published CSP data and publicly available spectra to compile a large sample of measurements of spectroscopic parameters at maximum light, consisting of pseudo-equivalent widths and expansion velocities of selected features for 232 CSP and historical SNe Ia (including more than 1000 spectra). Finally, we review some of the strongest correlations between spectroscopic and photometric properties of SNe Ia. Specifically, we define two samples: one consisting of SNe Ia discovered by targeted searches (most of them CSP-I objects) and the other composed of SNe Ia discovered by untargeted searches, which includes most of the CSP-II objects. The analyzed correlations are similar for both samples. We find a larger incidence of SNe Ia belonging to the cool and broad-line Branch subtypes among the events discovered by targeted searches, shallow-silicon SNe Ia are present with similar frequencies in both samples, while core normal SNe Ia are more frequent in untargeted searches.