Synchrosqueezing transform is a time-frequency analysis method with the reconstruction property， used as a post-processing step for the short-time Fourier transform （STFT）. This paper introduces two different methods of synchrosqueezing transform： the frequency-reassigned synchrosqueezing transform （SST） and the time-reassigned synchrosqueezing transform （TSST）. Their differences and applications are illustrated by comparing the STFT formula used by the two methods. For the numeral calculations， discretization implementation algorithms based on the two synchrosqueezing transform processes are provided. In this paper， the rubbing fault of the rotating machine and the impact fault of the bearing outer ring are used to validate the effectiveness of the two algorithms. Moreover， this paper points out that the SST method can better identify the rubbing fault in the rotating machine because of its characteristics of compressing the STFT coefficient in the frequency axis direction， and the TSST method can detect the impact fault frequency on the bearing outer ring because of its characteristics of compressing the STFT coefficient in the time direction.