"Nanoemulsions are kinetically stable" means liquids in the mixture will become separated very slowly. But the separation will happen eventually. "Microemulsions are thermodynamically stable" means the separation won't happen even waiting for a very very long time. Kinetic stability refers that from the reactant state (emulsion) to the product state (separated liquids) the reaction barrier is very high, but the free energy change is still negative (ΔG < 0). However, thermodynamic stability means the free energy change from the reactant state to the product state are positive (ΔG > 0), which means the reaction will not happen if there is no external energy input.
"Nanoemulsions are kinetically stable" means liquids in the mixture will become separated very slowly. But the separation will happen eventually. "Microemulsions are thermodynamically stable" means the separation won't happen even waiting for a very very long time. Kinetic stability refers that from the reactant state (emulsion) to the product state (separated liquids) the reaction barrier is very high, but the free energy change is still negative (ΔG < 0). However, thermodynamic stability means the free energy change from the reactant state to the product state are positive (ΔG > 0), which means the reaction will not happen if there is no external energy input.