There are two types of nuclear bombs:
1. Ones that depend on fission, like atomic bombs
2. Those that depend on fusion, like hydrogen bombs
The first one get their explosive energy from the splitting of atoms in materials like uranium or plutonium, which takes place automatically.
On the other hand, hydrogen bombs, depends on the fusing together of atoms, to release much larger quantities of energy than atomic bombs.
Also the fusing requires very high temperatures, therefore atomic bombs are generally used as triggers for hydrogen bombs. Meaning that atomic bombs are a nuclear bomb, but every nuclear bomb isn't an atomic bomb.
Hope that helps :)
