Well...here are some quotes about giants talking presenting one of the first ideas Tolkien had about giants:
"At this point in the story the agents of Melko appear, the
Uvanimor, 'bred in the earth' by him (Uvanimor, 'who are
monsters, giants, and ogres', have been mentioned in an
earlier tale, pp. 75-6); and Tuvo protected Men and Elves from
them and from 'evil fays'. "
As we see here the giants are associated with ogres (also creatures of legend and myth in lotr), and are very interestingly presented as creatures of Melkor.
and again in HOMe 6 the giants are associated with other evil creatures.
"Goblins were multiplying again and
reappearing. Trolls of a new and most malevolent kind were
abroad; giants were spoken of, a Big Folk only far bigger and
stronger than Men the [?ordinary] Big Folk, and no stupider,
indeed often full of cunning and wizardry. And there were vague
hints of things or creatures more terrible than goblins, trolls, or
giants. Elves were vanishing, or wandering steadily westward."
They were removed from the published
The Lord of the Rings and
The Silmarillion for a reason.
The giants were, like Beorn and everything in
The Hobbit originally, not written to be part of Tolkien's mythology. JRRT masterfully wove practically every aspect of
The Hobbit into
The Lord of the Rings and/or
The Silmarillion to give it a credible background, but the giants are one of those things that gave him trouble. They most definately existed, since Tolkien was not one to merely erase something completely, but they are no longer mentioned after
The Hobbit for a reason, most likely. They were written as fairy tale characters for when
The Hobbit was meant to be a children's tale for his young relatives and so did not fit with the epic setting of his greater mythology. The reference in
The Fellowship of the Ring is of a similar nature, although it is not Tolkien telling the fairy tale this time, but a Hobbit telling a far-fetched tale. That's my idea on it.
However, as I said in my first post in this thread one could speculate and expand the story from the Hobbit and think that they inhabited an area in the Misty Mountains. If so I would see them as a type of Men. Just as Hobbits were smaller, Giants could be a larger type of Men. I guess it all depends on your point of view.