One of the most important products of solar flares is nonthermal energetic particles, which may carry up to 50% of the energy released in the flaring processes. In radio observations, nonthermal particles generally manifest as spectral fine structures with fast frequency-drifting rates, named as solar fast-drifting radio bursts (FDRBs). This work demonstrated three types of FDRBs, including type III pair bursts, narrowband stochastic spike bursts following the type III bursts, and spike-like bursts superimposed on a type II burst in an X1.3 flare on 2014 April 25. We find that although all of them have fast frequency-drifting rates, they are intrinsically different from each other in frequency bandwidth, drifting rate, and statistical distribution. We suggest that they are possibly generated from different accelerating mechanisms. The type III pair bursts may be triggered by high-energy electron beams accelerated by the flaring magnetic reconnection, spike bursts are produced by the energetic electrons accelerated by a termination shock wave triggered by the fast reconnecting plasma outflows impacting the flaring loop top, and spike-like bursts are possibly generated by nonthermal electrons accelerated by moving magnetic reconnection triggered by interaction between coronal mass ejection and the background magnetized plasma. These results may help us to understand the generation mechanism of nonthermal particles and energy release in solar flares.