More than 3000 spectroscopically confirmed Type Ia supernovae (SNe Ia) are presented in the second data release (DR2) of the Zwicky Transient Facility survey. In this paper we detail the spectral properties of 482 SNe Ia near maximum light, up to a redshift limit of z ≤ 0.06. We measured the velocities and pseudo-equivalent widths (pEW) of key spectral features (Si IIλ5972 and Si IIλ6355) and investigated the relation between the properties of the spectral features and the photometric properties from the SALT2 light-curve parameters as a function of spectroscopic sub-class. We discuss the non-negligible impact of host galaxy contamination on SN Ia spectral classifications, and we investigate the accuracy of spectral template matching of the DR2 sample. We define a new subclass of underluminous SNe Ia (04gs-like) that lie spectroscopically between normal SNe Ia and transitional 86G-like SNe Ia (stronger Si IIλ5972 than normal SNe Ia, but significantly weaker Ti II features than 86G-like SNe). We model these 04gs-like SN Ia spectra using the radiative-transfer spectral synthesis code TARDIS and show that cooler temperatures alone are unable to explain their spectra; some changes in elemental abundances are also required. However, the broad continuity in spectral properties seen from bright (91T-like) to faint normal SN Ia, including the transitional and 91bg-like SNe Ia, suggests that variations within a single explosion model may be able to explain their behaviour.