  In this paper, we present a sample of 21 repeating fast radio bursts (FRBs)
detected by different radio instruments before September 2021. Using the
Anderson--Darling test, we compared the distributions of extra-Galactic
dispersion measure ($DM_{\rm E}$) of non-repeating FRBs, repeating FRBs and all
FRBs. It was found that the $ DM_{\rm E}$ values of three sub-samples are
log-normally distributed. The $DM_{\rm E}$ of repeaters and non-repeaters were
drawn from a different distribution on basis of the Mann--Whitney--Wilcoxon
test. In addition, assuming that the non-repeating FRBs identified currently
may be potentially repeators, i.e., the repeating FRBs to be universal and
representative, one can utilize the averaged fluence of repeating FRBs as an
indication from which to derive an apparent intensity distribution function
(IDF) with a power-law index of $a_1=$ $1.10\pm 0.14$ ($a_2=$ $1.01\pm 0.16$,
the observed fluence as a statistical variant), which is in good agreement with
the previous IDF of 16 non-repeating FRBs found by Li et al. Based on the above
statistics of repeating and non-repeating FRBs, we propose that both types of
FRBs may have different cosmological origins, spatial distributions and
circum-burst environments. Interestingly, the differential luminosity
distributions of repeating and non-repeating FRBs can also be well described by
a broken power-law function with the same power-law index of $-$1.4.
