The stellar velocity ellipsoid (SVE) in galaxies can provide important information on the processes that participate in the dynamical heating of their disc components (e.g. giant molecular clouds, mergers, spiral density waves, and bars). Earlier findings suggested a strong relation between the shape of the disc SVE and Hubble type, with later-type galaxies displaying more anisotropic ellipsoids and early types being more isotropic. In this paper, we revisit the strength of this relation using an exhaustive compilation of observational results from the literature on this issue. We find no clear correlation between the shape of the disc SVE and morphological type, and show that galaxies with the same Hubble type display a wide range of vertical-to-radial velocity dispersion ratios. The points are distributed around a mean value and scatter of σz/σR = 0.7 ± 0.2. With the aid of numerical simulations, we argue that different mechanisms might influence the shape of the SVE in the same manner and that the same process (e.g. mergers) does not have the same impact in all the galaxies. The complexity of the observational picture is confirmed by these simulations, which suggest that the vertical-to-radial axis ratio of the SVE is not a good indicator of the main source of disc heating. Our analysis of those simulations also indicates that the observed shape of the disc SVE may be affected by several processes simultaneously and that the signatures of some of them (e.g. mergers) fade over time.