A comprehensive study is given to short gamma-ray bursts (sGRBs) in the third Swift/BAT GRB Catalog from December 2004 to July 2019. We examine in details the temporal properties of the three components in the prompt gamma-ray emission phase, including precursors, main peaks and extended emissions (EE). We investigate the similarity of the main peaks between one-component and two-component sGRBs. It is found that there is no substantial difference among their main peaks. Importantly, comparisons are made between in the single-peaked sGRBs and the double-peaked sGRBs. It is found that our results of main peaks in Swift/BAT sGRBs are essentially consistent with those in CGRO/BATSE ones recently found in our paper I. Interestingly, we suspect, besides the newly-found MODE I/II evolution forms of pulses in BATSE sGRBs in paper I, that there would have more evolution modes of pulses across differently adjacent energy channels in view of the Swift/BAT observations. We further inspect the correlation of the main peaks with either the precursors or the EEs. We find that the main peaks tend to last longer than the precursors but shorter than the EEs. In particular, we verify the power-law correlations related with peak fluxes of the three components, strongly suggesting that they are produced from the similar central engine activities. Especially, we compare the temporal properties of GRB 170817A with other sGRBs with EE and find no obvious differences between them.
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