Unlike what Webster seems to believe, a detonation is not just any explosion - it is a very specific explosion.
There are two different types of explosion; namely deflagration, and detonation.
Black powder, for example will never detonate: when it burns, the oxidant (KNO3 / Potassium Nitrate) releases oxygen, which causes the fuel (C / carbon, normally) to burn faster, which releases more oxygen etc. This chain reaction propagates throughout the mixture in a very quick manner, during which hot gasses expand very fast. When the container this mixture is kept in (A gun barrel with a bullet, or a fire cracker, for example) cannot hold the pressure anymore, causing an explosion in the form of the rapid expansion of pressurised gas. In the case of a gun, the bullet flies out of the barrel, and in the case of the fire cracker, it is blown to smithereens with a satisfying bang - deflagregation.
When we talk about detonation, however, we are no longer talking about low explosives like gasses or gunpowders, but about high explosives such as nitroglycerine.
If you were to set fire to nitroglycerine, it will start burning quite merrily - deflagration*. However, if you want nitroglycerine to detonate, you need to start a chemical reaction which breaks the molecular structure of the high explosion. This is where blasting caps come in: to start a detonation.
During a detonation in, say, a stick of dynamite, explosive molecules are hit by the blast cap, which sets the chain-reaction going: Once the actual detonation starts, the entire stick is instantly turned into a gel-like plasma, which contains absurd amounts of pressure - up to 100,000 bar.
Comparing a detonation of a stick of dynamite to a black powder-filled firecracker or a deflagration is like comparing a shotgun to a bb-gun or a cork gun - the powers involved are barely comparable.
*) Something that is deflagrating can under some circumstances unpredictably detonate. Do not set fire to high-explosives unless you know what you are doing