The spontaneous emission of light by a substance not resulting from heat is luminescence (a type of cold-body radiation). $\ce{^1}$
A few types of luminescence are:
- Bioluminescence: Made by living creatures such as fireflies, glow-worms, and many marine creatures.
- Chemoluminescence: made by a chemical reaction. Glow sticks work this way.
- Electroluminescence: made by passing electricity through something like in a light emitting diode (LED).
- Photoluminescence: made by shining light at "luminous" (phosphorescent) paints.
- Röntgenoluminescence: made by shining X-rays at things. (The curious name comes from Wilhelm Röntgen (1845–1923), the discoverer of X-rays.)
- Sonoluminescence: made by passing energetic sound waves through liquids.
- Thermoluminescence: made when photons are emitted from hot materials.
- Riboluminescence: made by rubbing, scratching, or physically deforming crystals.
Phosphorescence: photoluminescence as a result of triplet-singlet electronic relaxation (typical lifetime: milliseconds to hours)
A chemical absorbs and then re-emits a photon of light, where the energy of the photons matches the available energy states and allowed transitions of the chemical takes place. In phosphorescence, the electron that absorbs the photon undergoes intersystem crossing $\ce{^2}$ into a triplet state.
The excited in triplet state returns to the lower energy singlet state. Such transitions, are kinetically unfavored and progress at a slow rate. Most phosphorescent compounds are fast emitters with triplet lifetimes in milliseconds. If triplet lifetimes are minutes or even hours, very slow degradation occurs.$\ce{^3}$ $\ce{^4}$ In phosphorescent materials, there's a delay between them absorbing energy and giving out light.These substances are so-called "glow-in-the-dark" materials.
To make glow-in-the-dark toys manufacturers mix zinc sulfide or strontium aluminate with plastic giving in glow-in-the-dark toys.$\ce{^5}$ $\ce{^6}$
Fluorescence
Fluorescent materials produce light instantly, when the excited atoms return to normal, in as little as a hundred thousandth of a second.$\ce{^4}$ $\ce{^7}$
Chemoluminescence
In the case of chemiluminescence, two chemicals interact which giving energy as a byproduct in the form of light( heatless glow).
When glow sticks are bent, an inner glass tube is broken releasing hydrogen peroxide. Hydrogen peroxide reacts with diphenyl oxalate giving 1,2dioxetanedione, which is unstable. It decomposes to carbon dioxide releasing energy. The energy is absorbed by electrons in dye molecule, that falls down to ground state releasing energy in the form of light.$\ce{^8}$ $\ce{^9}$

Chemiluminescence can happen naturally as well. In such instances — like fireflies — it is bioluminescence.
Some creatures, such as fireflies and jellyfish, contain chemicals within them that cause them to glow. Some of these creatures glow for protection, camouflage or to attract mates.
Ex 1.Bobtail squid $\ce{^12}$ $\ce{^13}$

Ex.2 Mycena lampadis ( mushrooms )$\ce{^14}$

The principal chemical reaction in bioluminescence involves some light-emitting molecule and an enzyme, generally called the luciferin and the luciferase.$\ce{^10}$ $\ce{^11}$ $\ce{^15}$
Electrochemiluminescence $\ce{^16}$is a special form of chemiluminescence in which the light-emitting chemiluminescent reaction is preceded by an electrochemical reaction.$\ce{^17}$
References
1 https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Map%3A_Principles_of_Instrumental_Analysis_(Skoog_et_al.)/15%3A_Molecular_Luminescence_Spectrometry
2 https://www.shsu.edu/chm_tgc/chemilumdir/JABLONSKI.html
3 https://en.wikipedia.org/wiki/Intersystem_crossing
4 https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/lumin1.htm
5 http://www.phys.ubbcluj.ro/~dana.maniu/OS/BS_7.pdf
6 https://science.howstuffworks.com/innovation/science-questions/question388.htm
6 https://www.wonderopolis.org/wonder/how-do-things-glow-in-the-dark
[7] https://en.wikipedia.org/wiki/Fluorescence#Lifetime
[8] https://www.compoundchem.com/2014/10/14/glowsticks/
[9] https://en.wikipedia.org/wiki/Glow_stick#Fluorophores_used
[10] https://en.wikipedia.org/wiki/Bioluminescence#Chemical_mechanism
[11] https://www.nationalgeographic.org/encyclopedia/bioluminescence/
[12] https://www.nationalgeographic.org/encyclopedia/bioluminescence/
[13] https://en.wikipedia.org/wiki/File:Sepiola_atlantica.jpg
[14]https://www.timeforkids.com/g34/bioluminescence-2/
[15] http://photobiology.info/Branchini2.html
[16] https://www.sciencedirect.com/topics/chemistry/electrochemiluminescence
[17] https://www.sciencedirect.com/science/article/pii/S0008622317304943