Thermodynamic stability applies to a particular system. The reactivity of a chemical substance is a description of how it might react across a variety of potential chemical systems and, for a given system, how fast such a reaction could proceed.
Chemical substances or states can persist indefinitely even though they are not in their lowest energy state if they experience metastability - a state which is stable only if not disturbed too much.  A substance (or state) might also be termed "kinetically persistent" if it is changing relatively slowly (and thus is not at thermodynamic equilibrium, but is observed anyway). Metastable and kinetically persistent species or systems are not considered truly stable in chemistry.  Therefore, the term chemically stable should not be used by chemists as a synonym of unreactive because it confuses thermodynamic and kinetic concepts. On the other hand, highly chemically unstable species tend to undergo exothermic unimolar decompositions at high rates. Thus, high chemical instability may sometimes parallel unimolar decompositions at high rates.