This investigation presents a comprehensive comparative analysis of negative specific heat phenomena manifested in two fundamentally distinct astrophysical systems: black holes and stellarclusters. Through rigorous theoretical examination and synthesis of contemporary observationalevidence, we elucidate the underlying physical mechanisms governing negative heat capacity inthese systems. Our analysis reveals that black holes exhibit negative specific heat through quantumthermodynamic processes at the event horizon, as described by the Bekenstein-Hawking formulation and Hawking radiation theory. Conversely, stellar clusters demonstrate this phenomenonvia classical gravitational thermodynamics and the gravothermal catastrophe. While both systemsexhibit similar thermodynamic behavior, the fundamental physics, characteristic timescales, andobservational manifestations differ substantially. Black holes demonstrate quantum-mechanicalnegative heat capacity with timescales exceeding the age of the universe, whereas stellar clustersexhibit classical negative heat capacity observable on galactic evolutionary timescales. Thesefindings contribute significantly to our understanding of gravitational thermodynamics, stellardynamics, and the fundamental nature of entropy in gravitational systems, with implicationsextending to quantum gravity, cosmology, and the thermal evolution of astrophysical structures.