They are routinely called small tactical nukes. The current testing, design and technology is focused on smaller nukes, not for large globe busting nukes. It's the wave of the future for nukes......
It's a bit late to go link hunting. But a good place to start is www.fas.org The Federation of American Scientists site. They even have a page up already on the N. Korean program.
Yes, that thing on the end is actually a nuclear bomb, a model W54 warhead. Yield could be dialed between 0.02 and 1.0 kilotons. That's 1/750th to 1/15th the size of the Hiroshima bomb.
Here's the same warhead packed as a nuclear "land mine", for demolition:
The nuke is the small item on the *left* -- the larger item in the middle is its packing/carrying case.