This is not how it works. Containment structures prevent the actual core materials from exiting the reactor, since those are heavy metals with high radioactivity and long half lives. The latest reports suggest that the reactor pressure vessel (RPV) in Unit 2 is likely breached, but this is inside the primary containment vessel (PCV).
In both the Three Mile Island and Fukushima incidents, radioactive steam was vented to the atmosphere. Additionally at Fukushima a breached pressure vessel probably leaked radioactive water into the primary containment vessel. This water was pumped out (into spent fuel storage, I think). I've also heard concerns that the spent fuel pools were feared to be leaking into the ocean, but so far as I know that hasn't happened enough to cause alarm.
The radiation inside the containment structure where the Unit 2 RPV breached is really high, "dead in a couple hours" levels. Outside the reactor buildings (the red dots on the map in your second link) background radiation levels didn't rise any higher than the natural background radiation in parts of Kerala, India, and in several other places around the world. Much higher than normal for Japan, sure, but nothing dangerous. Those levels can be explained by the Iodine and Cesium isotopes in the vented steam.
Calling these happenings a "containment failure" is disingenuous at best. The 50-year-old containment structures at Fukushima appear to have done exactly the job they were designed to do, after a magnitude 9 earthquake no less.
Confinement of radioactive material and control of radioactive releases
As a result of the damage to the reactor cores in Units 1–3, large amounts of steam and hydrogen escaped the reactor pressure vessels. This, in turn, pressurized and heated the primary containment vessels. These vessels were breached and steam, hydrogen and other gases, together with radioactive material, were released into the reactor buildings and eventually to the environment. The primary containment vessels of the reactors had not been designed to withstand the pressure that could be generated in a severe accident; because of this, venting systems had been installed in the 1990s [22, 23] to limit the pressure in the containment vessels in the event of an accident. There are indications that the primary containment vessels for Units 1–3 failed at various stages in the progression of the accident. This was the result of the pressure and temperature in the primary containment vessel rising to levels that were far in excess of their designed capability before venting could be implemented (see Section 2.1). The leakage of radioactive material from the reactor cores was partially mitigated by the suppression pools, which retained some of the radionuclides released from the reactor pressure vessels.
That should be clear enough.
The radioactive water problem is huge. It was not "pumped into spent fuel storage". Several large tank farms were built to store it, along with a processing plant to remove radioactive solids. Some of it did leak into the Pacific Ocean.
Exactly what I described in less alarming words. Steam, hydrogen, other gases, and "radioactive material" (Iodine and Cesium in the steam) are not the same thing or anywhere near as dangerous as actual melted fuel and corium escaping containment. Conflating this with the idea of molten core materials breaching containment is extremely irresponsible.
I'm not entirely sure about the radioactive water situation, and it sucks to hear that it may be worse than I thought. Do you have a source confirming the extent of contaminated water that ended up in the ground or ocean? It's really hard to find anything unambiguous here, tons of stories about "leaks" but many of those reports are actually about leaks into the reactor buildings. As far as I can tell a very large number (trillions?) of becquerels went into the Pacific Ocean right around the time of the tsunami, and since then no water outside the reactor complex has been measured with radiation levels outside regulatory limits (although they've been pumping groundwater collecting in the basements into big tank farms, like you said). It does look like the large volume of water pumped into the ocean initially (to make room for contaminated core water in the spent fuel pools, like I said) may have accumulated in bottom-feeding fish near the site. And it looks like there may be water from the site leaking into the ocean at some rate (although not enough to make any ocean water unsafe to drink). Other than that all I can find is an enormous volume of noise and fearmongering.