Quora answer by Raj Arjit:
These are commonly used terms, but technically speaking these are different.
1. Ignition refers to the process / phenomena of initiating the overall burning (burning used loosely here) process.
2 and 3. Combustion and burning are similar in the respect that both leads to the formation of new species as a result of chemical reaction in a irreversible process.
Combustion and burning are different in the respect that combustion technically refers to a – when the process is being done in “fixed” amount of air/oxygen. Burning refers when the process has access to infinite amount of air/oxygen i.e. done in open.
4. Explosion happens when rapid increase in volume takes place imparting momentum to the reaction particles with a production of a subsonic shock wave.
5. Detonation is similar to explosion with the difference lying in the fact that the rapid increase in volume is so high that production of supersonic shock wave takes place. (See the image carefully, you can see the wave arc in top)