According to "Singing Tips: Falsetto vs. Head Voice," in artspace2000.com, falsetto is a light voice production limited in power and variation of tone. Falsetto is also called "false voice," and can sometimes be so weak that it sounds like strained whispering.
Among the most famous bands that employs the falsetto regularly is the BeeGees. As noted in "How the Voice Works" in Musemuse.com, falsetto is often used when a person is trying to sing along to a song that is beyond their range. It is also frequently used by backup singers.
Head voice has a more vibrant tone than falsetto, and engages the vocal cords to a greater extent, as noted at become-a-singing-master.com. In head voice, the vocal cords are close together, giving it a fuller sound than falsetto, in which the cords are separated.
Head voice is often used in church music or choral music. Head voice should not be confused with the similar term in opera, which is a different style of singing.
According to Vocalist.org.uk, it is possible to move from falsetto to head voice, or to use falsetto in order to increase the strength of head voice.