Oh my God! The ignorance is astounding.
There are two general types of nuclear weaponry available. Fission bombs and fusion bombs.
Fission is "splitting".
Fusion is "welding".
"Fission" is the process of splitting a single nucleus into two pieces. The nucleus of the atom contains all the protons in the atom. These are positively charged particles that repel each other when seperated by a distance via electrostatic forces, but which can be bound together in the nucleus via the "strong nuclear force".
This binding takes energy, so the mass of a nucleus is less than the sum of the masses of the combined protons and neutrons (an electrically neutral particle). The energy needed to hold the nucleus together is equivalent to the missing mass, via Einstein's E = MC^2 formula.
Atomic nuclei are not static collections of marbles, but dynamic waves. The largest atoms are not stable and decay radioactively. The uranium atom, and others, can also spontaneously split into two roughly equal halves. Once these halves start to get outside the range of the strong nuclear force, the electrostatic force flings them away. The energy released in this process used to be the energy needed to bind the nucleus together. Also, the splitting isn't perfect and stray neutrons are released.
These are two isotopes of uranium. An isotope of an element has the same number of protons but a different number of neutrons. All uranium atoms have 92 protons in their nucleus, while U235 has 143 neutrons and U238 has 146. It turns out that Uranium isotope 235 is more sensitive to neutrons than U238.
It also turns out that U238 is about 200 times more common than U235. To make effective reactors or to make uranium based bombs, it is necessary to refine uranium and "enrich" the U235. Almost all isotopes are chemically identical and the enrichment processes are purely mechanical and difficult. That's why it's been taking Iran forever to get their first bomb. (I'm hoping we give them one of ours first).
Back to bombs. It was discovered a chain reaction of fissions can be created, where one fission creates two or more neutrons that go on to create more fissions in a rapidly multiplying chain that can result in enormous energy release. This chain reaction is the heart of the fission bomb.
A fission bomb, like those donated to Japan, needs only to get enough fissionable material close enough together to start the reaction. The longer the material can held together, and the more material that can be included, will drive the strength of the bomb.
But all you need to know is that fission is effective with heavy elements, and involves reducing those atoms to smaller pieces.
A fusion bomb works the opposite way. You take two light nuclei and jam them together. This will also release energy when the strong nuclear force is able to overcome the electrostatic repulsion of the nuclei and bind them together. Hydrogen happens to be the easiest element to work with, hence our fusion bombs are also called "hydrogen" bombs.
To create fusion on an industrial scale, it's necessary to heat masses of hydrogen to millions of degrees and yet contain it so the atoms stay close enough to interact. A fission bomb primer charge is used for this.
Two things combine to make fusion bombs more powerful than fission bombs. The first is that fusing hydrogen to make a helium atom release a lot more energy than the fission of a uranium atom.
Then there's a physical limit to how much uranium can be forced together to interact in a chain reaction before the force of the reaction blows the mess apart. The Teller-Ulam configuration of the hydrogen bomb traps the hydrogen in a tamper and there's no theorectical upper limit to the size of a fusion bomb, though moving them becomes difficult.
That's it. Two kinds of nuclear weapons. All other explosives release chemical energy.