I felt it best to make a video for this point. I looked at many of the Youtube videos that deal with this question, and I found most of them to be inaccurate, to say the least. Some actually had the distinction backwards, and others tell very little, perhaps so that you will want to take a lesson to learn more?
This video has a very specific scope: On the pitches F4-A4, what kinds of singing would be called “head” (or one of its synonyms) as contrasted with “falsetto” (or one of its synonyms)?
Some other terms for what I call “head voice” in this video include: full voice, full head voice, voce piena in testa, and mix. It is a label for the manner of singing notes in and above the passaggio in a coordinated manner with both chest register and higher register involvement.
Some other terms for what I call “falsetto” in this video include: heady head, disconnected head, unsupported head, and breathy head. Falsetto is the name many people give to the higher pitches in the male range that do not sound or act like a continuation of the chest register. Falsetto has more air flow, fewer overtones and cannot blend into chest voice easily.
A major goal of many male singers in classical, rock, musical theatre, pop, R&B, Gospel, and choral styles is how to smooth out the transition to higher notes and to sing them with power, rather than cracking into the weaker, less masculine sound of falsetto.