Chemiluminescence vs. Bioluminescence
Doesn't that also have to do with chemical reactions but inside living organisms?


Exactly! That's why there is one scientific society for both phenomena: ISBC - International Society for Bioluminescence and Chemiluminescence ;-)

The thermal reactions, that lead to an excited species which eventually emits a photon are quite similar. From a reactive compound, typically called a luciferine, a four-membered ring, often a dioxetanone is formed. This decarboxylates and gives rise to a molecule in an electronically excited state. In reality, the decarboxylation is often not just a spontaneous process but requires an activator. W. J. Baader at IQUSP in Sao Paulo, Brazil has examined that in great detail.

The luciferines can be quite different compounds, such as  


diaryloxalates (these are used in glow sticks, where the diferent colours come from diferent fluorphores that absorb the initial photon and emit at different wavelength)  
benzothiazole derivatives (firefly)  
triazine derivatives (marine organisms)