I would say that fantasy encompasses everything fantastic that cannot fit in other fiction.  It's a nice name for the gray areas, where suspension-of-belief in general fiction ends.  I like it because it brings that other emotion, Wonder, so vividly and wonderfully into being.  It has no boundaries, which is what is so wonderful and horrible about it.  The writer may fly, and then again become lost, because there are no stop signs.

I think this thread will be discussed in Platonic terms.

I've read somewhere that High Fantasy involves unrealistic white soaring towers, etc--which the very worst will usually have, and a couple dozen dragons, and too many capital letters--but I've also read them at their best.  High Fantasy is perhaps the brightest (is that a good word?) of the categories, slightly more light-hearted.  A foray into dreams?

Medieval Fantasy is almost exactly opposite.  The world is painted in varying shades of muck and gray, which can become powerful in contrast to the fantastic element.  The tendency is to remain in the muck, however.

Dark Fantasy is the foray into nightmares.  I am terrified of nightmares; I tend to avoid these.  I went through the Year's Best looking for the stories without the initials E.D.

Tithe and de Lint are Urban Fantasy.  That category's never really struck me as stuffy; but then, I don't live in a city; what would I know?

Is this what you like?

Ooooh!  I read Pratchett!  He belongs in the "Pratchett" category, I agree, along with all the other Pratchetts who've popped up in his wake.
     If you expanded Fantasy to include science fiction that is not technically science fiction, you could put D.Adams in the "Pratchett" category and rename the category "Pratchett-Adams."

     For sheer gorgeousness, there's Patricia A. McKillip and Pamela Dean.  McKillip's earlier works are, compared to what she's written these past ten years, poor stuff.  Her Riddlemaster trilogy borrows heavily from Tolkien, which is possibly the only reason I respect Tolkien.  I've only read Dean's Rosemary, Juniper, and Gentian and Tam Lin, but both are spectacular.  The only detriment is a short, unsatisfying ending, which I overlook for the sake of the rest of the book.  It's a strange philosophy.

     I read all fantasy--but only finish the good books--and historical fic, and (mostly historical) mystery, and short stories, and poetry.  Right now, Chaucer and Plato.