Using Sloan Digital Sky Survey (SDSS) spectra, we applied an automatic method to search for outflows (OFs) in three large samples of narrow-line active galactic nuclei (AGN) at low redshifts (z < 0.4), separated into three spectral activity classes: radio-loud galaxies (RGs), 15,793; radio-quiet Seyfert 2 AGN (Sy2), 18,585; and LINERs, 25,656. In general, the probability of detecting an OF decreases along the sequence Sy1→Sy2→LINER/RG and independently of the AGN class, the wind velocity, traced by W80, increases with the AGN luminosity. Moreover W80 is systematically higher in RGs or any of the other AGN classes when detected in radio. These results support the idea that there are two main modes of production of OF, the radiative mode dominant in radio-quiet AGN and the jet mode dominant in RGs, although both modes could also happen simultaneously at different levels. From the spectra and SDSS photometry, the characteristics of the AGN host galaxies and their supermassive black holes (SMBHs) were also retrieved using the stellar population synthesis code STARLIGHT. This revealed that, independently of the AGN spectral class, (1) galaxy hosts with OFs have systematically later morphological types and higher star formation rates (SFRs) than their counterparts without OF, (2) the AGN occupy different positions in the specific diagnostic diagram (specific black hole accretion rate (sBHAR) versus specific SFR), which suggests they follow different evolutionary paths congruent with the morphology of their galaxy hosts, and (3) they show no evidence of AGN quenching or triggering of star formation. These results are consistent with a scenario explaining the different AGN classes as consequences of different formation processes of galaxies: early-type galaxies (LINERs and RGs) formed bigger bulges and more massive SMBHs, exhausting their reservoir of gas more rapidly than late-type galaxies (Sy2 and Sy1), and thereby quenching their star formation and starving their SMBHs.