Different Types of Nuclear Weapons

Fission (A-Bombs) are the most basic nuclear weapon and are incorporated into the other weapon classes. This bomb's power comes from splitting heavy nuclei (plutonium and uranium) with neutrons; as the uranium or plutonium split each atom releases great amounts of energy - and more neutrons. The daughter neutrons cause an extremely fast nuclear chain reaction.

Fission bombs are the only type of nuclear bomb used in war so far. The development of fusion bombs has relegated the 'straight fission' bomb to history. All weaponized nations now possess Fusion bombs.
Fusion (H-Bombs), using the incredible heat of a fission bomb 'spark plug', compress and heat deuterium and tritium (isotopes of hydrogen) which fuse, releasing immense amounts of energy. Fusion weapons are also known as thermonuclear weapons since high temperatures are required to fuse deuterium and tritium; such weapons are usually many times more powerful than the bombs that destroyed Nagasaki and Hiroshima.
EMP Weapons. A nuclear weapon detonated at a very high altitude will generate an electromagnetic pulse so powerful that it can destroy electronic and electrical devices. Placing radios, flashlights in a SEALED metal container (a "Faraday cage") may protect from EMP, providing the items being protected are not in contact with the enclosure. The metal shield must surround the protected item completely - and it helps if it is grounded.

The items to be protected should be insulated from the conductive shell, since the EMP field washing over the shield can still induce voltages in solid state circuit boards. A metalized "space blanket" (costing about $2.00 USD) wrapped securely around a device wrapped in newspaper or cotton may act as an ineffective Faraday shield, helpful if one is far from the blast.

Another method is to wrap a cardboard box copper, or aluminum foil. Place the item in there and plug the device into the ground.
Other Types. Nuclear science is kept secret for reasons of national security, so this list is not neccessarily exhaustive. Outside of science fiction, real scientists have speculated ways to create EMP weapons without nuclear blasts, create Cobalt-Salted ("Neutron") bombs to increase immediate radiation presence, and possibly other types.