In this study, we addressed the ongoing debate about what burnout and depression scales measure by conducting an exploratory structural equation modeling (ESEM) bifactor analysis. A sample of 734 U.S. teachers completed a survey that included the Center for Epidemiologic Studies Depression scale (CES-D-10), the depression module of the Patient Health Questionnaire (PHQ-9), the Generalized Anxiety Disorder scale (GAD-7), and the Maslach Burnout Inventory (MBI), which contains emotional exhaustion (EE), depersonalization (DP), and (diminished) personal accomplishment (PA) subscales. Job adversity and workplace support were additionally measured for the purpose of a nomological network analysis. EE, burnout’s core, was more highly correlated with the depression and anxiety scales than it was with DP and PA, even with controls for item content overlap. The CES-D-10, PHQ-9, GAD-7, and EE subscale of the MBI were similarly related to job adversity and workplace support. ESEM bifactor analysis revealed that the CES-D-10, PHQ-9, GAD-7, and EE items loaded highly on a general factor, which we labeled nonspecific psychological distress (NSPD). We conclude that depression, anxiety, and EE scales reflect NSPD. DP items largely reflect two factors, NSPD and depersonalization, about equally. PA items were found to be less related to NSPD. With respect to the debate surrounding burnout-depression overlap, our findings do not support the view that the burnout construct represents a syndrome that consists of EE, DP, and diminished PA and excludes (or does not primarily include) depressive symptoms.