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A dirty nuke is simply a ground burst. Air bursts have most of the radioactive material dispersed into the upper atmosphere, and it spreads around the world at levels your body handles every day. Ground bursts leave the radioactive material stuck to things, and much more of it stays. People got sick for a while after Hiroshima, but it's still a city and they still live there. A ground burst would mean not living there for centuries or more.

In I think our first nuclear tests after WWII, we did an air drop ("Baker") over captured ships and other ships that we didn't need anymore. It was a mile off-target. Ships were spread out even farther than that, but the results weren't that spectacular. Then the "Charlie" test had a nuclear bomb on a cable 50 feet underwater beneath a transport. When that went off, the ship rode the blast a mile into the air before disintegrating, and a mountain of water came down on everything. There were battleships and carriers that survived both blasts, but when they came back to them the second time, the water stayed kind of hot and men were getting sick from being on those ships for too long. They couldn't wash the radioactivity off, and one of the worst things was that barnacles on the sides were actively filtering radioactive waste from the water and holding it against the ships.

There is a balance, though. Ground bursts leave the best concentrations of radiation, but it takes an air burst to get a good blast radius.

The dirty bomb is none of these. It just blows up the side of maybe one building, but the debris from it will be spread all over and be very poisonous for a long time.

Typically, a "dirty-bomb" is a low-yield nuclear bomb that releases cobalt-60 and iodine-131 as byproducts. These have a long half-life (60 years or so) and would render the area inhospitable to life for several generations. You could design one to result in both massive devastation and longterm toxicity. The bomb would be normally set off as a conventional device using TNT, PETN, or even a lot of C4. A small version of an A-bomb can be equipped to release cobalt-60 and iodine-131 as well. Since it releases radiation, it can be termed a nuclear device, even though it may or not be a fission or fusion bomb. This is a scary situation. Let's hope the reports are untrue. I would expect that is such a device is detonated here in the USA, that it would leave us no choice but to retaliate with SLBMs at Afghanistan. I do not know if we still even have ICBMs.

"A dirty nuke is simply a ground burst."

A ground burst is definitely a dirty nuke, but a "crude nuke" built by terrorists would have a higher ratio of radioactive isotopes generated to blast effect, and so is "dirtier" than a more sophisticated weapon. Of course, any such crude bomb would probably ALSO be set off on the ground, so the "dirty effect" would be magnified compared to blast.