Accurately capturing drought change is particularly important in the face of climate change, especially given the need to understand the influence of temperature changes on drought under different climatic conditions. In this study, we compared two drought indices, the Standardized Precipitation Index (SPI) based only on precipitation and the Standardized Precipitation Evapotranspiration Index (SPEI) based on precipitation and temperature, across global arid and humid regions for the period from 1991 to 2020. Through multi-scale analysis of gridded climate data spanning 1- to 24-month timescales, we systematically investigated how temperature influences drought characterization across arid and humid regions. Key findings reveal fundamental divergences in drought detection: while SPI and SPEI show strong agreement in humid regions (R-2 > 0.80), their correlation declines sharply along the aridity gradient, reaching complete divergence (Delta = -100 %) in hyper-arid zones. The SPEI identifies 22-35 % more drought events than the SPI in arid/semi-arid regions, with differences magnifying at longer timescales (24-month, r = 0.58). Moreover, trend analysis demonstrates that SPEI-detected drought intensification occurs twice as rapidly as SPI trends in critical agricultural zones (-0.14 vs. -0.07), implicating rising temperatures in accelerated aridification. Notably, most semi-arid regions show significantly stronger drying trends in the SPEI, highlighting the index's enhanced sensitivity to climate change impacts. These results challenge the use of precipitation-only indices in water-limited ecosystems, demonstrating that SPI underestimates drought frequency by 18-27 % and severity by 1.2-2.3 standardized units in drylands. Our study highlights the critical need of weighting temperature effects according to regional climatic conditions, with immediate implications for early warning systems in a changing climate.