Originally there was the atomic bomb, or A-bomb, whose source of energy was the fission of uranium-235 or plutonium-239. These weapons were very large, very heavy, and not very powerful in comparison to their successors because little of the fission fuel was actually consumed. The weapon self-destructed too quickly.
Just a few years later, scientists developed a more efficient "boosted" fission device that used a small amount of fusion to increase consumption of the fission fuel. The fuel for fusion was a mixture of deuterium and tritium gases, which are isotopes of hydrogen. Specifically it's the fusion of one deuterium atom and one tritium atom that makes things go. (The fact that tritium has a short shelf-life because of radioactive decay is a complication in actually deploying a weapon with tritium.) But it's important to understand that nearly all the energy released by a boosted fission device still comes from fission; the fusion simply generates more neutrons that, in turn, cause a greater percentage of the uranium or plutonium to undergo fission. The additional energy released by the fusion reactions is relatively small. Nearly all fission weapons today — whether standalone weapons or triggers for H-bombs (see below) — are boosted. However, a rogue nation or terrorist group starting from scratch would probably develop a non-boosted fission weapon first and then pursue a boosted fission weapon.
And then we come to the hydrogen bomb, or H-bomb, or thermonuclear device as it's called in professional circles. This weapon relies on fusion for most of its energy. A different fusion fuel is used, lithium deuteride, which is a solid and relatively stable compound. A thermonuclear device uses a small fission device (usually a boosted fission device) as a trigger to create the heat, pressure, and neutrons that are prerequisites for fusion to begin. The neutrons cause the lithium to produce tritrium, and then the tritium fuses with the deuterium. These thermonuclear weapons can grow quite large by increasing the amount of lithium deuteride. Improvements in missile navigation, however, have led to reductions in the individual size of these weapons. For example, the U.S. formerly fielded thermonuclear bombs of 10-25 megatons. All warheads of U.S. weapons today are less than 1 megaton. Contemporary missiles will almost always hit within a few hundred yards of their targets. You don't need a multi-megaton explosion with that kind of accuracy.
Lastly, scientists discovered that if they added passive uranium-238 to the thermonuclear device, they could significantly increase the energy produced by the weapon because the fusion would cause the normally placid uranium-238 to undergo fission with a high degree of completeness. In such a weapon about half the energy comes from fusion and half from fission. These are the types of weapons that the U.S. and the Soviet Union were (and still are) prepared to launch at one another. They have the highest yield per pound of weapon.
So what did the North Koreans actually detonate? Most experts believe it was a boosted fission weapon — or that's the story we are being given. They offer the explanation that a true thermonuclear device would have produced larger effects, such as ground tremor. Perhaps they're right. But even if they are, it's still a worrisome development because the North Koreans have taken another step.