Abstract Fast radio bursts (FRBs) are mysterious radio bursts with a time scale of approximately milliseconds. Two populations of FRB, namely repeating and non-repeating FRBs, are observationally identified. However, the differences between these two and their origins are still cloaked in mystery. Here we show the time-integrated luminosity-duration (Lν-wint, rest) relations and luminosity functions (LFs) of repeating and non-repeating FRBs in the FRB Catalogue project. These two populations are obviously separated in the Lν-wint, rest plane with distinct LFs, i.e., repeating FRBs have relatively fainter Lν and longer wint, rest with a much lower LF. In contrast with non-repeating FRBs, repeating FRBs do not show any clear correlation between Lν and wint, rest. These results suggest essentially different physical origins of the two. The faint ends of the LFs of repeating and non-repeating FRBs are higher than volumetric occurrence rates of neutron-star mergers and accretion-induced collapse (AIC) of white dwarfs, and are consistent with those of soft gamma-ray repeaters (SGRs), type Ia supernovae, magnetars, and white-dwarf mergers. This indicates two possibilities: either (i) faint non-repeating FRBs originate in neutron-star mergers or AIC and are actually repeating during the lifetime of the progenitor, or (ii) faint non-repeating FRBs originate in any of SGRs, type Ia supernovae, magnetars, and white-dwarf mergers. The bright ends of LFs of repeating and non-repeating FRBs are lower than any candidates of progenitors, suggesting that bright FRBs are produced from a very small fraction of the progenitors regardless of the repetition. Otherwise, they might originate in unknown progenitors.