We study a complete and distance-limited sample of 25 LINERs, 21 of which have been imaged with the Hubble Space Telescope to study their physical properties and to compare their radio and optical properties with those of other samples of local AGNs, namely Seyfert galaxies and low-luminosity radio galaxies (LLRG). Our results show that the LINERs population is not homogeneous, as there are two subclasses: i) the first class is similar to LLRG, as it extends the population of radio-loud nuclei to lower luminosities; ii) the second is similar to Seyferts, and extends the properties of radio-quiet nuclei towards the lowest luminosities. The different nature of the various classes of local AGN are best understood when the fraction of the Eddington luminosity they irradiate, Lo/LEdd, is plotted against the nuclear radio-loudness parameter: Seyferts are associated with relatively high radiative efficiencies Lo/LEdd ≳ 104 (and high accretion rates onto low mass black holes); LLRG are associated with low radiative efficiencies (and low accretion rates onto high black hole masses); all LINERs have low radiative efficiency (and accretion rates), and can be radio-loud or radio quiet depending on their black hole mass.