In consideration of your question, I came across extensive blogs on vocal pedagogy by Ian Howell, a professional countertenor and educator in Boston. Since I'm not familiar with his work, I cannot tell you whether his writings are authoritative or not, but he has written extensively on the physiology of the countertenor voice and what is being done with the vocal folds (cords). Here is a blog post with thoughts on your question.
Countertenor Technique: An Introduction to Concepts by Ian Howell
Countertenors are more common today than ever before. They have always been around in the British tradition, where you frequently find men singing alto in choirs. You also find British countertenors in small all-male vocal ensembles like the King's Singers and Chanticleer in the USA. But you hear countertenors more and more in contemporary Baroque ensembles ("early music" or "historically-informed performance" or groups that perform on "period instruments"). I work with one such nationally-renowned professional Baroque chamber orchestra in the USA (I do their publicity and marketing) and I have met a few countertenors. I'm working on a concert with a famous countertenor that will be given on May 5, 2013. I may have the opportunity to ask our countertenor (who has perfromed lead roles in opera houses all over the New World and Europe) a few questions.
Generally the term "countertenor" is only used for singers doing classical music, particularly, as I mentioned, either the Baroque music originally written for castrati, or certain music of any historical period in the British tradition. However, the basic techniques can be found all over rhythm and blues and rock music. Smokey Robinson, Prince, and Justin Hawkins of the British rock group The Darkness, among many others, at times certainly make use of a falsetto register and vocal timbre that is not far removed from what classical countertenors achieve. Justin Timberlake and Freddie Mercury have been known to swoop into that range. You can make the argument that Brian Johnson of AC/DC (who has a deep bass speaking voice) is a kind of counter-tenor. He only ever sings in falsetto. There are many other singers in pop music who at least dabble in this.