In an effort to understand the puzzle of classifying gamma-ray bursts (GRBs), we perform a systematic study of {it Swift} GRBs and investigate several short GRB issues. Though short GRBs have a short ($lesssim2$ s) prompt duration as monitored by the Burst Alert Telescope, the composite light curves including both the prompt and afterglow emission suggest that most of the short GRBs have a similar radiative feature to long GRBs. Further, some well-studied short GRBs might also have an intrinsically long prompt duration, which renders them as a type of short GRB imposters. Genuine short GRBs detected by {it Swift} might be rare that discriminating the observed short GRBs is, not surprisingly, troublesome. In particular, the observational biases in the host identification and redshift measurement of GRBs should be taken with great caution. The redshift distribution which has been found to be different for long and short GRBs might have been strongly affected by the measurement methods. We find that the redshifts measured from the presumed host galaxies of long and short GRBs appear to have a similar distribution.