Properties of bars and bulges in the Hubble sequence are discussed, based on an analysis of 216 disc galaxies of S0-Sm types (S0s from the Near-Infrared S0 Survey and spirals from the Ohio State University Bright Spiral Galaxy Survey). For this purpose we have collected, and completed when necessary, the various analyses we have previously made separately for early- and late-type galaxies. We find strong evidence of pseudo-bulges in all Hubble types. Pseudo-bulges are disc-like structures formed by secular evolutionary processes in galaxies. Similar to spirals, the early-type disc galaxies (S0-S0/a) have on average relatively exponential bulges with Sersic index n < 2, and 56 per cent of them show disc-like fine structures in the region of the bulge. For some of the galaxies there is also kinematic evidence of pseudo-bulges. If S0-S0/a galaxies were once spirals, stripped of their gas, then redistributed gas and star formation in the disc would be a natural explanation for all pseudo-bulges in the Hubble sequence. However, it is difficult to explain how the bulges of S0 galaxies, which typically include about 30 per cent of the total galaxy mass, were formed by secularly induced central star formation. A more likely explanation is that pseudo-bulges in barred early-type galaxies are a combination of secularly induced star formation and the central steepening of the old stellar distribution. Bulges in non-barred early-type galaxies could be either classical merger-built bulges, or pseudo-bulges formed by similar processes as in barred galaxies, but in response to massive ovals or lenses (70 per cent of S0-S0/a galaxies have ovals/lenses). Observational support for the outlined picture comes from the fact that bars in early-type galaxies seem more evolved: their bars are long and massive and frequently (40 per cent) have ansae morphologies. In this scenario it would be possible also to explain why barred early-type galaxies (preferentially pseudobulges) have slightly smaller B/T flux ratios than the non-barred early-type galaxies (mostly classical bulges).