The Quick Trick: If you're standing in an absolute wasteland amid thousands of corpses, it was a nuclear bomb. If you're standing in a normal city street amid a moderate amount of inconvenience, it was a dirty nuclear bomb.
The Explanation: Here is the primary difference: Nuclear bombs have, in the past 70 years, killed hundreds of thousands of people. Dirty nuclear bombs have, in all of human history, killed exactly no one—partly because they aren't terribly dangerous and partly because not one has ever been detonated.
Conventional nuclear weapons get their explosive power from either nuclear fission or fusion. The bombs dropped on Hiroshima and Nagasaki—the only nuclear weapons that have been used in warfare—were both fission bombs. Fusion bombs, sometimes called hydrogen bombs, are even more powerful—the U.S. once detonated a 15-megaton fusion bomb in a test. That's approximately 100 times more powerful than "Little Boy," the nuclear weapon dropped on Hiroshima that instantly killed 100,000 people. Most modern bombs combine fission and fusion: a small fission bomb is used to create heat adequate to fuel the
Even with the physics know-how, the bombs require exceedingly rare isotopes of either plutonium or uranium. The process of getting the elements to the necessary isotope is known as enrichment, and enrichment is generally the stumbling block for nations looking to join the nuclear club. It was even a challenge for the U.S.: Almost 90 percent of the Manhattan Project's budget was spent enriching uranium.
In short, nuclear weapons are extremely difficult to make—and we hope they always will be. A dirty nuclear bomb, on the other hand, could be made by a reasonably smart 14-year-old with access to hospital equipment. Dirty bombs combine conventional explosives (say, dynamite) with radioactive materials (say, cesium, which is used in radiation treatment for cancer patients). Almost all scientists believe that even in the case of a well-designed dirty bomb, the explosive would cause much more damage than the radiation. The fact is there just aren't any acquirable materials radioactive enough to cause much fallout. And while it could be very expensive and inconvenient to clean up an urban area after a dirty bomb attack—that's about it. The difference between the two is that conventional nuclear weapons are infinitely more worrisome.
The only recorded attempt to detonate a dirty bomb came in 1995, when Chechen rebels—who had been on the forefront of terrorism techniques since the Soviet Union's breakup—called reporters to say they'd planted a bomb in a Moscow park. Made of dynamite and cesium taken from a cancer treatment center, the dynamite might have killed people, but its cesium would have been just the equivalent of a few X-rays for those walking past the park. Regardless, the bomb was defused before it exploded.