The other type is called an "interstadial". They are less than 10,000 years long, and they occur "irregularly". For the most part no one has any idea why any particular "interstadial" happened.
At the present time it is possible we are 5,000 years past the end of the last Interglacial, with the extra time technically being an interstadial which could end tomorrow once the conditions causing it change.
Interstadials are highly important to humanity. The warm period referred to in the news story above is not an "interglacial" but an "interstadial". It lasted a few thousand years, the oceans rose, it went away, the water went back to the poles as ice and snow ~ probably powered a glacial advance in the North American ice sheet in fact.
Another "interstadial" about 35,000 years ago allowed Cro Magnon man to enter Europe. It lasted a while. Things went cold again. The Neanderthals died out, and possibly the original Cro Magnons who moved to Europe died out leaving only a small remnant population hanging onto the Franco-Spanishborder region.
Going the other way around there are sometimes short-lived periods of glaciation within the framework of an interglacial. The Younger Dryas appears to have been one such. The Little Ice Age was probably another ~ and it may not be over.
At some point we will tip over into the next glacial period and billions of people will die.
Greenland and Antarctic ice core data suggests we are so close to that point that we could find the snows piling up just any time.