To help understand the difference, think of the nuclear fuel and waste at Fukushima as being like a whole bunch of lights packed together, all blazing at full brightness. With the shielding (water) now gone, the light is blazing out of the plant into the environment. This is the first kind of leak, gamma rays spreading outwards. These rays are highly concentrated right by the plant, and are strong enough at this point to cause real injury to people nearby.
The cloud of material spreading from the plant is like a few of the lights being blown out of the plant—continuing to glow as they are carried away. Very quickly, the lights become isolated from one another. Instead of a raging blaze, the situation is more like a whole bunch of little twinkles arcing across the Pacific.
What will these isolated, spreading, radioactive atoms do to human health? We can use the experience and data gathered from Chernobyl to help figure that out.
In the Chernobyl accident, about half of the radioactive elements released were various radioactive noble gasses—chemically related to Radon, these atoms are chemically inert and rapidly disperse into the environment. Iodine-131 made up about 12% of the radioactive atoms released. Cesium-137 and Strontium made up about half a percent apiece.
Radioactive Iodine, cesium and strontium can replace the non-radioactive iodine, potassium and calcium in our bodies. Because living things scavenge and concentrate these radioactive elements, some of the physical dilution caused by the cloud spreading is reversed as the elements enter the food chain. Even hundreds or thousands of miles away from the plant, these radioactive elements could be found in the bodies of Europeans surrounding Chernobyl.
This sort of radiation exposure is quite different than being blasted by gamma or x-rays. Instead of causing immediate injury, this low-level but chronic radiation exposure increases the chance of bad things—primarily cancers. This change in risk can be thought of in the same way as the change in risk caused by smoking, or driving a car without a seatbelt.
The strongest risk of elements released from a nuclear power plant causing cancers is with Iodine-131. The radioactive Iodine-131 from Chernobyl settled on grass that was eaten by cows. The cows, in turn, secreted the radioactive Iodine into their milk. The milk was then consumed by people, and the radioactive Iodine was concentrated in their thyroids. Those—particularly children—exposed to Iodine-131 (by this pathway, or others), ended up getting Thyroid cancers at a dramatically higher rate than you'd expect. By 2000 (14 years after the disaster), there were about 4000 cases of Thyroid cancer that could be directly attributed to the radioactive Iodine released by Chernobyl.
Iodine-131 has a short half-life of only about eight days. Within about five half lives (or 40 days) after the leaks are finally contained at Fukushima, the risk from Iodine should abate. Here in North America, the concentrations of Iodine-131 should be too low to cause any health effect—even in the worst imaginable situations. Save the Potassium Iodine pills for the people in Japan who really need them.
Cesium and Strontium were both spread by Chernobyl, and detectable in the bodies of Europeans. Despite this, no studies have shown an increased risk from these exposures of cancers or other negative health effects. Our bodies are quite good at dealing with infrequent, long-term radiation damage—able to repair DNA if provided enough time between hits. Strontium and Cesium both have long half-lives (about 30 years), meaning they decay very infrequently—perhaps giving out cells enough of a chance to repair the damage before injury occurs.