I get the this question a lot actually. And it’s like asking ‘What is the difference between a cardiac muscle and a heart?’
Two names for the same thing.
Conventionally speaking, ‘falsetto’ and ‘head voice’ are two names for the same vocal resonance. And both names are wrong and misleading, respectively.
Falsetto being the traditional word for it, derived from the Latin word ‘Falso’ meaning ‘false’. In other words, False Voice. Which of course is ludicrous because it isn’t false. It is obviously your own voice, just different than usual.
The name ‘head voice’ is actually closer to accurate, if misleading.
In reality each person has only one voice with one set of vocal cords (folds) producing vibrations known as sound. So, your voice is your voice. Period.
However, you can manipulate the resonance of the sound produced by your voice using your jaw, tongue, and various throat/mouth muscles that have long scientific names that don’t need to be addressed here to get the point across.
It is easier to help visualize the resonance by dividing it up into sections and giving it a name based upon its general area of resonance. Thus the name ‘head voice’ was born because the resonance is happening generally in the area of the head.
But, if you have a brain, there is no resonance happening in the head. It is happening mostly in your nasal passages/cavities.
So, the name for that resonance would be most accurately named the ‘Nose Voice’. I go over all of this in the 4th Element of Singing – Resonance module of my online video courses on learning how to sing.
But if you want to use the words ‘falsetto’ or ‘head voice’, either one will work. They are referring to the same thing.
Nasal resonance – The Nose Voice.