Mythologically, there’s pretty much no difference between dryads and hamadryads. If there is any, it’s pretty much splitting hairs, with hamadryads being somewhat more integrally tied to their trees. But if you give something two names, it's an excuse for role-players to create two monsters. (Which I fully support, by the way. See my rant on oreads. But anyway…) In Tall Tales of the Wee Folk, for instance, hamadryads are dryads who spontaneously arose out of trees, whereas dryads are the daughters of dryads and hamadryads who have to seek out a tree of their own to bond with.
In Pathfinder, a hamadryad is essentially super-dryads—queen of the entire forest rather than a single tree, and not bound to her ward. Alone, she (with the aid of the dryads and trees in her charge) can tend the health of nearly every acre in her care. When paired with an erlking sibling or spouse, they form a yin and yang of nature’s gifts—its patience and its passion, its stillness and its speed, its healing touch and savage bite.
An ancient forest covers the land bridge between Elurian and Kitsunar. And where the two continents meet, so too do the spirits of those lands—which is how the hamadryad Querquetulania fell in love with the jinushigami Muk. But spirit love operates by different rules…and when a winter erlking (see Pathfinder Adventure Path #68: The Shackled Hut for the winter fey template) trespasses in the forest, his supernatural influence turns a helpless Querquetulania and her dryad handmaidens hateful and xenophobic. Muk is outraged, of course (though in the slow, glacial manner of his kind) and concerned fey and kami of both woodland courts recruit adventurers to free the hamadryad from the corrupted erlking’s control before war rips the great forest apart.
The hamadryad Magnolia has a home forest. She just chooses to ignore it, apparently. Instead she runs a myrtle-shrouded teahouse and clinic in the Seventh Ward. She guards the secret of her race carefully, however, and will attempt to silence those who probe too closely (usually via call lightning storm, summoned creatures, or by creating treant assassins with liveoak). The reason she has taken up city life has something to do with the crossed scimitar and shillelagh hanging over her fireplace (and guarded by sentinels that are not readily apparent to mortal eyes) and a particular paving stone in her garden that is actually a stone table from legend.
A hamadryad is losing her memory. A being of ancient age, she is fast losing her recollections of the present day, spending more and more time locked in the primeval memories of her past. In her confusion, she summons dinosaurs, mammoths, and frost giants to comfort her and drive off the humanoids that “infest” her lands. Adventurers become involved when sightings of dire tigers and tyrannosauruses become too common to ignore.
—Pathfinder Bestiary 4 148
I don’t give two coprolites about college basketball, but my grad school alma mater does make some nice videos.
Oh, and the dress was really made of displacer beast hide, so it was black and blue and white and gold, but then disappeared because it wasn’t Open Game Content.