The difference between atomic powerplant and atomic bomb is that in atomic powerplant, (more specifically, in atomic reactor), the chain reaction is controlled. There the heat is exposed slowly and continuously. Unnecessary heat is exploited by water and get rid of. In this case, the activity of the reactor can be increased as well as stopped.
On the other hand, in atomic bomb, the chain reaction is really fast and uncontrolled. So a huge amount of energy is created in a very short time and explosion occurs.
Atomic explosion is not possible in atomic powerplant. Because for explosion, high amount of (more than 80%) Uranium enrichment is needed. In atomic bomb, there is no system to exploit the neutrons and the critical mass of Uranium is put in a very conjusted place.
In modern atomic powerplants, low scale enriched (3-5%) Uranium is used. Controller rod is always present in the active zone. These rods are consisted of neutron exploiting agents like Boron. Also compression of fuel is also possible in these plants.
The Chernobyl accident was non-atomic. It occured because of the pressure of the extra vapour stored inside the reactor. The explosion of Fukushima-1 powerplant occured because of air and Hydrogen getting mixed. Also if judged from the scale of explosion, these could never be compared with any atomic bomb explosion.