I think this description of a countertenor is helpful in understanding how the voice is used. Most countertenors use a falsetto or head voice, but they do come in all shapes and sizes, so it’s not “one size fits all” type of voice - basically like almost all voice types. I got this from Wikipedia, but my opera/music text books pretty much describe it in the same way.:
"A trained countertenor will typically have a vocal centre similar in placement to that of a contralto or mezzo-soprano.[12] Peter Giles, a professional countertenor and noted author on the subject, defines the countertenor as a musical part rather than as a vocal style or mechanism. In modern usage, the term “countertenor” is essentially equivalent to the medieval term contratenor altus (see above). In this way, a countertenor singer can be operationally defined as a man who sings the countertenor part, whatever vocal style or mechanism is employed.[13] The countertenor range is generally equivalent to an alto range, extending from approximately G or A3 to E5 or perhaps F5. In actual practice, it is generally acknowledged that a majority of countertenors sing with a falsetto vocal production for at least the upper half of this range, although most use some form of “chest voice” (akin to the range of their speaking voice) for the lower notes. The most difficult challenge for such a singer is managing the lower middle range, for there are normally a few notes (around Bflat3) that can be sung with either vocal mechanism, and the transition between registers must somehow be blended or smoothly managed.[14]
In response to the (in his view) pejorative connotation of the term falsetto, Giles refuses to use it, calling the upper register “head voice.”[15] Many voice experts would disagree with this choice of terminology, reserving the designation “head voice” for the high damped register accompanied by a relatively low larynx that is typical of modern high operatic tenor voice production. The latter type of head voice is, in terms of the vocal cord vibration, actually more similar to “chest voice” than to falsetto, since it uses the same “speaking voice” production (referred to as “modal” by voice scientists), and this is reflected in the timbre.[16]
Other authorities would prefer to restrict use of the term countertenor to singers employing little or no falsetto, equating it with haute-contre and the Italian term tenor altino.[17] Russell Oberlin was himself a countertenor of this type, noted for his ability to sing alto and/or countertenor parts extending above C5 (the notorious “tenor high C” popularized by Italian opera) while still employing modal voice (many high tenors, particularly those who specialise in the bel canto repertoire of Rossini, Bellini, Donizetti, and their contemporaries can also do this, but generally use a more robust voice production). Some writers insist that this can only be accomplished physically by a man in possession of vocal cords considerably shorter than average,[18] and that such a singer would therefore possess an unusually high speaking voice (a falsettist countertenor normally speaks as a baritone or bass). Like the haute-contre, these tenorial countertenors have a lower range and tessitura than their falsettist counterparts, perhaps from D3 to D5. Those authorities who hold that only non-falsettists are “real” countertenors would prefer the phrase “male alto” for the more common falsettist type.[19]
Some falsettist countertenors have a much higher range, approaching that of a coloratura soprano. These are usually called sopranists or simply “male sopranos”. [20] There are in addition a few rare adult male singers who, for hormonal or other physical reasons, did not undergo the voice-change associated with male puberty, and are referred to as endocrinological castratos.[21]"
I can sing into the mid alto range without straining. I don’t think this is falsetto.