Here's what the book has to say. There's intentionally a ton of room for players to put their own spin on the setting.
The Three Shards of the Elven People
The Elf Queen wears a crown of three parts: black amethyst and obsidian for the dark elves, green emerald and flowering plants for the wood elves, and diamond and force magic for the high elves. When the elves were truly unified, they referred to themselves as the three branches of the elves, but since the war with the dwarves it became customary to refer to themselves as the three Shards of the Crown.
Even though her crown remains whole, the Queen herself uses the term. At first she used it sardonically, chiding her people for their animosities. But words used sarcastically have a way of sticking if they're true, and the shorthand method of referring to one of the three branches of the elves is to call them shards.
Dark Elves
Within the Queen's Court, the dark elves are referred to by the name they use for themselves, the Silver Folk. Outside the Court, the use of the term Silver Folk is extremely polite, or ironic. Most surface dwellers refer to them as dark elves or drow, interchangeably.
Dark elves are not uniformly evil. Drow society varies from entirely evil to merely cruel. That said, it's almost a point of pride among dark elves that some of the world's greatest villains have come from their race, to the point that even a goodly hearted drow may end up arguing that her race's despotic overlord was far more powerful than another race's former tyrant.
Use the flavor of evil you like best for dark elves and allow your players with drow characters to be part of groups from the fringe or isolated settlements that differ from the norm. Compared to the dark elves of some fantasy worlds, the Silver Folk can be trusted to the extent that they are mostly loyal, in some strange or disgusting way, to their Queen. The Queen's critics point out that it takes a twisted and capricious monarch to engage the affections of the dark elves—you can't win when you are Queen of three feuding races.
High Elves
The high elves are sometimes called light elves. Their term for themselves means both high and light. Humans hearing that description often supply "sky" as a better translation and are told "No, either high or light, not sky," which is apparently reserved for creatures of the overworld. High elves in your game might have markedly different eyes when they've been using magical power, and you can call them by whatever name works best for you.
Wood Elves
The wood elves are known as the gray elves in the oldest texts, but they grew out of the name, which appears to have been an early Elf King's idea of a logical transition between light and dark. Some humans call them the green elves. Wood elves resisted that name until recently, when some wood elves associated with the High Druid began using the term "green elf," or "wild elf," to distinguish themselves from elves who do not follow the High Druid. Green and wild are presently considered impolite terms at the Court of Stars.
Elven Woods
What outsiders think: Elven woods are full of giant trees. Their coloration starts as normal brown on the fringe, but may be white, silver, red, or golden as you go deeper into the forest. Wood elves in the area will usually know if outsiders are present. High elves sometimes live among these woods, near the center of the forest, and dark elves can occasionally be found there as well.
What elves know: The perfect elven wood is a harmonious three-part city in the key of nature. Wood elves live in and among the great trees, in tents pitched around the trunks or in more permanent houses set high in the branches.
The dark elves live in the giant caverns and twisting labyrinths carved out within and below the great trees' roots. The spiral towers of the high elves rear above the green canopy. The lives of the three Shards of the Crown are mostly separate, but together they weave magic that strengthens the wood and increases every elf 's fortune.
That's the dream at least. In practice, the harmony between the three elven shards broke after the war with the dwarves. Elven woods still have all three layers of elves, at least in sections of the woods. But few such woods are populated throughout, and if wood elves and high elves populate the trees and towers, it's unlikely that the dark elves will live beneath them. Conversely, where dark elves are prosperous, high elves may be able to live by keeping their distance in the high towers, but wood elves are likely to be scarce.
Without harmony between the three shards of the elves, their perfect woods are seldom perfectly maintained. High elves may perform astrological observations from their high towers, or, just as likely, gargoyles will be using the ruins of the towers as lookout perches for an evil cult. Wood elves may dwell within the trees' high branches, or the hunters that track their prey among the forest may be bugbears and dragons. Dark elves may cluster with their spiders in temples and arenas below the trees' roots, or the catacombs in those deep places may be populated by owlbears and ghosts.