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Fast Radio Bursts (FRBs) are the short, strong radio pulses lasting several milliseconds. They are subsequently identified, for the most part, as emanating from unknown objects at cosmological distances. At present, over one hundred FRBs have been verified, classified into two groups: repeating bursts (20 samples) and apparently non-repeating bursts (91 samples). Their origins, however, are still hotly debated. Here,we investigate the statistical classifications for the two groups of samples to see if the non-repeating and repeating FRBs have different origins by employing Anderson-Darling (A-D) test and Mann-Whitney-Wilcoxon (M-W-W) test. Firstly, by taking the pulse width as a statistical variant, we found that the repeating samples do not follow the Gaussian statistics (may belong to a chi-square distribution), although the overall data and non-repeating group do follow the Gaussian. Meanwhile, to investigate the statistical differences between the two groups, we turn to M-W-W test and notice that the two distributions have different origins. Secondly, we consider the FRB radio luminosity as a statistical variant, and find that both groups of samples can be regarded as the Gaussian distributions under the A-D test, although they have different origins according to M-W-W tests. Therefore, statistically, we can conclude that our classifications of both repeaters and non-repeaters are plausible, that the two FRB classes have different origins, or each has experienced distinctive phases or been subject to its own physical processes.