Critical mass equals no explosion

If you were awake in physics class, you might remember being told that an atomic bomb works on the principle of critical mass. The theory goes that when critical mass is reached, that is to say, when you have a large enough blob of fissionable material, you will get a sustainable chain reaction. Then the chain reaction causes an explosion, and you blow up Hiroshima or Nagasaki. The Wikipedia article linked above warns:

      "Until detonation is desired, a nuclear weapon must be kept subcritical."

There have been several 'criticality accidents' over the years. They release radiation in the form of heat and light, but no explosion. Even the explosion at Chernobyl was not caused by a nuclear explosion: 

    "On 26 April 1986 at 1:23 a.m., reactor 4 suffered a massive, catastrophic power excursion (the chain reaction grew out of control, similar to the initial stage in the detonation of a nuclear weapon). This caused a steam explosion, followed by a second (chemical, not nuclear) explosion from the ignition of generated hydrogen mixed with air, which tore the top from the reactor and its building, and exposed the reactor core."

(Quote from the Wikipedia article linked above.)

At Chernobyl, the reactor core overheated, and turned the cooling water into steam. The steam caused the first explosion. 

Here is an historic account of a criticality accident:

The work was dangerous as well as time-consuming. One of the worst accidents involved Louis Slotin, a Canadian scientist in charge of monitoring plutonium chain reactions in a device known as the "guillotine." One day the Slotin's screwdriver got jammed in the guillotine, causing the plutonium to form a hypercritical mass capable of explosion. Immediately Slotin tore apart the two pieces of plutonium with his bare hands and in the process absorbed an enormous amount of radiation.

The event is accurately portrayed in the movie "Fat Man and Little Boy ".

The Atomic Bomb

An atomic bomb is supposed to work like this: There are several smaller pieces of fissionable material which are thrown together rapidly into one lump, which is large enough to be a critical mass. The critical mass undergoes a nuclear chain reaction which causes an explosion. 

If that is the case, then why didn't the incidents where a critical mass was reached in laboratories and nuclear reactors cause an explosion? And if a critical mass doesn't explode, then what caused the explosions at Hiroshima and Nagasaki?