An atomic bomb is an explosive device in which a large amount of energy is released through nuclear reactions. This makes an atomic bomb, more properly called a nuclear weapon, a much more powerful device than any conventional bomb containing chemical explosives.
Nuclear weapons are divided into two types: the fission weapon and the fusion weapon. Most weapons are fission devices, and they use uranium, or more probably plutonium, as the fissile fuel. Fusion weapons (sometimes called "hydrogen bombs" back when they were first being developed) use a conventional fission bomb to initiate a fusion reaction. This results in a greater yield when the weapon detonates. A larger blast means increased blast radius and more damage, as you have probably already guessed.
The atomic bombs were Little Boy, Fat Man and Thin Man.