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There is a wide consensus that defendants convicted at trial receive a harsher average sentence than similar defendants who plead guilty. In the literature, some researchers name this disparity as the "trial penalty," while others name it as the "plea discount." A closer look at existing theoretical and empirical works suggests that these two terms actually have different underlying assumptions, and therefore require different modeling techniques. More importantly, theories also suggest that variables related to the size of trial penalties are not necessarily related to that of plea discounts, and vice versa. We use empirical data to demonstrate the differences in the modeling and explanation of the two terms.