There are a lot of differing opinions about what Head Voice and Falsetto are. Some use the terms interchangeably while others consider them to be different things.
I am one that thinks of them as different. For me Head Voice is a true voice that is generally associated with the higher range, although it can be brought down through the middle range. In the pure form it does lack completeness sufficient for performance. This is why it generally needs to be reinforced by the connection to the energy of our breathing.
Falsetto feels to me like an attempt at Head Voice but lacking the clean vibration of the vocal cords. The resulting sound is more breathy and lacking clarity. This is because the glottis doesn’t close completely allowing the breath to pass through unvocalized.
The essence of how I define the registers is what set of muscles are closing the glottis and adjusting the vocal folds for vibration. In chest voice it is muscles in the body of the folds. Which give more bulk and stiffness.
In head voice it is the muscles that draw the folds longer, bringing them close together through an elastic stretch. Falsetto is an attempt at vocalization without these muscles being sufficiently active.
Watch this video to see examples and further explanation. Thanks!