What is the distinction between "graduate school" and "professional school"? I have previously been involved with mentoring high school students as well as undergraduates, who typically don't have a clear understanding of all of the career possibilities available to them and how they might pursue them. 

One of the distinctions I typically make is that "Professional School" (e.g. medical, law, physicians assistant, nurse practitioner, dental) is further training past undergraduate studies that prepares you for entry into a very specific profession/job with a terminal degree. "Graduate School" is additional training that prepares you to be an expert in a particular field, but the job opportunities are much more diverse and you may or may not be working toward a terminal degree. One of my college advisors made this distinction to me, and I have carried it forward. 

Is making this distinction between graduate and professional school correct? 
Is there another more specific or subtle difference that I am missing?

What is the true distinction between graduate and professional school? - Or is there not one?
At least in my geographic region (Texas, or the US southern states), a professional school implies a curriculum that targets specific skills for a particular vocation. In effect, this is akin to my awkward bastardization of several concepts:  


  "Teach a man to fish and he can become a fisherman ... help him learn
  how to think and he can pursue a career in whatever he wants."


The former refers to a professional/vocational school.  The latter refers to accredited universities with broader range of curriculum missions.  Granted, this reflects my biased perspective: admittedly, vocational schools have a (usually) noble and useful purpose, but proper universities can offer so much more to enrich the whole student, and potentially brighten the intellectual and career outlook for years to come.