I don't know the technical, scientific, psychiatric, or neurological differences between HFA and LFA. I'm sure there are folks here who could tell you exactly what the scientific literature says about that. But based on my experiences, the more verbal a person is, the more likely they are to be called high functioning regardless of sensory or behavioral issues which may be greater for the HFA than the LFA. It seems to me that in common practice and daily life among lay people, autistic people who can speak or communicate in writing are deemed high functioning.
The Carly's Cafe video tells the story of my LFA nephew. He cannot volunteer words, he rarely speaks except for echolalia and talking aloud to himself (self-talk), yet he is super bright, a math genius, has a great sense of humor and almost photographic recall of things he reads about like his special interests, likes to help me go grocery shopping so he can push the cart, earplugs and sunglasses in place of course, and cook food with me. But he struggles to tell me anything of substance and then it is only in response to my prompting him with questions. Multiple choice questions often work best for us to communicate with each other. He picks the best answer for himself but, of course, the choices he has are only my best guesses of what is really going on with him. His high intelligence is locked inside his head and no one has been able to help him find his voice. I just love him as he is, spend as much time as I can with him, even if we just sit on the couch with my nose in a book and his nose in the laptop reading Wikipedia, happy being together in companionable silence. But he cannot tell me in words what he is thinking or write what he is thinking. How can we reach him? Does he just not want to talk or does his brain structure preclude him ever being able to do that, or a little of both?