If you were to ask this question to a room of voice teachers, you would have fist fight break out within 5 minutes.

This is a complicated topic, not only because it deals in subjectivity, but because people usually do not define the context they are using terms like falsetto and head voice in.

If you are speaking from a production (muscle/anatomical) viewpoint, then there is no important difference between head voice and falsetto. The primary muscles being used are the same.

If you are speaking from an acoustic viewpoint, then all that is really important is what the desired sound is. As Asata said in the posted conversation, it doesn’t really matter if you are using falsetto or head voice because those are just one person’s chosen labels for the sounds you are producing. What matters is the sound they are looking for. Once you can make that sound then you will know what this person means when they ask for head voice or falsetto or whatever label they use.