The magnitude-frequency distribution (MFD) quantifies the relative frequency of large versus small earthquakes, serving as a critical tool for investigating earthquake dynamics and assessing seismic hazard. The classic Gutenberg-Richter (GR) model posits that earthquake occurrences follow an exponential decay. The tapered Gutenberg-Richter (TGR) distribution, a variant of the GR model, assumes a reduced frequency of larger earthquakes. It might be a more appropriate model, as there should be a physical upper limit to the magnitude of both natural and induced seismicity. Distinguishing these two distributions is important not only for a better understanding of earthquake physics but also for both precise estimation of the MFD parameters and robust forecasting of earthquake magnitudes. We therefore evaluate various methods which can be used to differentiate these two distributions and their statistical significance given a set of observations. We find the likelihood-ratio test to be the most effective approach and demonstrate that the probability of correctly identifying the TGR catalog exceeds 90% when the corner magnitude is one unit smaller than the maximum magnitude predicted by the GR distribution. Furthermore, we introduce an objective framework aimed at detecting potential temporal shifts between the two distributions. We apply this framework to revisit several observational cases, including global earthquakes and induced seismicity. We observe diverse behaviors of MFD and significant temporal variations. Some of these signals may imply special earthquake physics, while others can be the artifacts of catalog generating.