I have that feeling a lot when I read news reports about nuclear reactors and radiation, most recently this article in the New York Times. The way the authors refer to radiation suggests to me that there's a lot they don't understand about it. And that, then, makes me wonder what else they've got wrong.
Radiation is a particular type of energy. Sunlight is radiation. Your microwave oven uses radiation. Heat is radiation. Because the understanding of this kind of radiation was developing at the same time that nuclear radiation was being discovered, the word got extended to energy emitted by unstable atoms. That energy includes x-rays (called gamma rays in relation to nuclear energy) and also energy carried by particles emitted by those atoms: helium nuclei (alpha radiation), electrons (beta radiation), and neutrons.
What reporters seem to lose track of, or perhaps never understood, is that nuclear radiation is inextricably connected to a certain kind of matter. Sometimes they make it sound like an all-enveloping condition, or something that suddenly appears out of nowhere.
The Japanese Nuclear and Industrial Safety Agency said that as many as 160 people may have been exposed to radiation around the plant, and Japanese news media said that three workers at the facility were suffering from full-on radiation sickness.A nuclear reactor emits gamma rays and neutrons when it's running and afterwards. In the case of Fukushima, it appears that fuel elements have been damaged and some of the radioactive material inside them has gotten out. There are two different things that "exposed to radiation" could mean. One is that a person has been too close to the reactor or inside the shielding that protects workers from the neutrons and gamma rays. The other is that the person has been in contact with radioactive material. The material could be on their skin, or they might have breathed it in or swallowed it. In either case, the exposure may be small or large. The consequences depend on what kind of exposure it was.
If three workers are suffering from "full-on radiation sickness," the probability is that they are brave people who volunteered to go inside the reactor shielding to fix something. The reactor is still contained, and there's no indication that there was a critical excursion, in which a great burst of neutrons and gamma rays might overwhelm the shielding.
The people outside who may have been "exposed to radiation" probably were downwind from a release of radioactive material (which includes gases) from the reactors. Some of that material may be in the form of particulates, and the people who were exposed may have that material on their skin, where it can be washed off (this is what is meant by decontamination), or in their lungs. The reason that iodine tablets are being distributed is that radioactive iodine is one of the fission products that could be released from the reactor. Radioactive iodine, when it's taken into the body, goes to the thyroid gland, where it can cause cancer. Taking non-radioactive iodine in those tablets loads up the thyroid so it won't absorb the radioactive iodine.
If the reports are accurate, the releases so far of radioactive material are small, and the damage and probability of later effects, like cancer, depend on the amounts of material people are exposed to.
Then there's the term "meltdown." It's what happened in the movie, "The China Syndrome," which seems to color all use of the word. But put "partial" in front of it, and it could refer to a few spots on a few fuel elements. It's been clear for some time (and I've been saying it), from the fission products that are being seen, that fuel elements are damaged, which could be cracking or melting from higher temperatures than normal. It also seems clear from the reports so far that the damage in Japan is much less than a total meltdown. There was a total meltdown of the core at Three Mile Island. But it showed that "The China Syndrome" was wrong: the melted material made its way less than an inch into the concrete containment. And hardly any of it was released from the containment. [This isn't quite right about Three Mile Island; see comments. But the point stands: Three Mile Island was probably worse than what is happening in Japan, and it wasn't as bad as people thought it could be.]
So I'd say "damaged fuel elements", but "meltdown" is much more exciting.
Not wrong, just not how someone who knows what they're talking about would say it.
Update: I see a question from someone who has googled in to this post. Can you "catch" radiation from someone who has been exposed? If it's a matter of being exposed to gamma rays or neutrons from a reactor, and there's no contamination, the answer is no. If someone has radioactive dust on their skin, it can rub or fall off and become attached to another person. How serious that is depends on how much radioactive material there is and if they breathe or swallow it.