What caused the problem at Chernobyl was that it went prompt critical - basically the worst thing a reactor could ever do. This happened after the operators attempted to run a flawed test under incorrect conditions. Due to the bad design the reactor went prompt critical. That means that while operating at power, it started changing power levels at a rate uncontrollable by humans, basically a runaway reaction where the power spiked far above the design. This flashed the water in the reactor into steam, which under extreme heat, had enough pressure to explode the 2000 ton covering off of the reactor, spreading the damaged fuel for miles.
Fukushima's reactors were shut down following the earthquake. There is enough to soak neutrons that the reactors cannot even start up, much less undergo the same kind of reaction that occurred at Chernobyl.