The atom bombThe A-bomb, short for atom or atomic bomb, uses fission, which basically means splitting. Neutrons released during the process cause a chain reaction, causing fission in more and more cells. In uranium and plutonium, the elements used in atomic bombs, the nuclei are unstable and easy to split which is why they are used.
In their natural state, uranium and plutonium atoms are constantly undergoing radioactive decay. The nuclei are spaced sufficiently far apart so that the destruction-causing chain reaction does not take place. However, if you concentrate and compact the process into a bomb, you have the weapon that effectively ended World War Two.
In the bomb dropped on Hiroshima, uranium was used to initiate fission, whereas plutonium was used in the Nagasaki bomb. It was devastating, causing hundreds of thousands of deaths from the initial blasts and illnesses for decades afterwards, and causing one the most determined fighting forces in history to immediately surrender. However, an even more powerful weapon was to make itself known to the world after the war.
The hydrogen bombThe hydrogen bomb, or H-bomb, is what caused the world to live in a state of constant edginess during the Cold War, as if living without smart glasses and Netflix wasn’t enough. H-bombs, also known as thermonuclear weapons, use the process of nuclear fusion; the process of forming a heavier nucleus from two lighter ones. This is done by heating hydrogen up to a tremendous temperature using an A-bomb to create the heat, in the first instance. The extreme temperature causes hydrogen to fuse into helium, releasing vastly more energy than the atom bomb process alone. All of this happens in about 600 billionths of a second.
See Which is more dangerous Atom bomb or Hydrogen bomb?