Fast Radio Bursts (FRBs) are millisecond-duration transient events that are typically observed at radio wavelengths and cosmological distances but their origin remains unclear. Furthermore, most FRB origin models are related to the processes at stellar scales, involving neutron stars, blackholes, supernovae, etc. In this paper, our purpose is to determine whether multi-structural one-off FRBs and repeaters share similarities. To achieve this, we focus on analyzing the relationship between the FRB event rate and the star formation rate, complemented by statistical testing methods. Based on the CHIME/FRB Catalog 1, we calculate the energy functions for four subsamples, including apparent non-repeating FRBs (one-offs), repeaters, multi-structural one-offs, and the joint repeaters and multi-structural events, respectively. We then derive the FRB event rates at different redshifts for all four subsamples, all of which were found to share a similar cosmological evolution trend. However, we find that the multi-structural one-offs and repeaters are distinguishable from the KS and MWW tests.