I recall that in The Hobbit, the company of Dwarves was captured by "Wood" Elves. I don't remember if LOTR mentioned Elves in any other way than "Elves". Is there more than a single type of Elf in the saga, or are they a single species?
While the answers provided in this negative elf question were informative, they did not answer my question.
There are three more kinds of Elves described in The Hobbit, in addition to the Wood-elves (emphasis mine):
The feasting people were Wood-elves, of course. These are not wicked folk. If they have a fault it is distrust of strangers. Though their magic was strong, even in those days they were wary. They differed from the High Elves of the West, and were more dangerous and less wise. For most of them (together with their scattered relations in the hills and mountains) were descended from the ancient tribes that never went to Faerie in the West. There the Light-elves and the Deep-elves and the Sea-elves went and lived for ages, and grew fairer and wiser and more learned, and invented their magic and their cunning craft, in the making of beautiful and marvellous things, before some came back into the Wide World.
The Hobbit Chapter 8: "Flies and Spiders"
All of these Elves, and more groups besides, are a single species1, and all Elves can trace their roots to Cuiviénen. Although there are many subdivisions among the Elves, they're based on history and geography rather than biology.
"The High Elves of the West", in the quote above, is a reference to the Calaquendi, the Elves who journeyed to Aman in the Years of the Trees, and the three groups named correspond to the three tribes of the Calaquendi:
But those are only the Elves who went to Aman; there are many more groups who didn't, of which the Wood-elves are one tribe:
The Avari (Dark-elves)2 The first sundering of the Elves occurred after they were invited to Aman; the ones who were unwilling to leave Middle-earth became known as the avari, meaning "unwilling" (emphasis mine):
Then befell the first sundering of the Elves. For the kindred of Ingwë, and the most part of the kindreds of Finwë and Elwë, were swayed by the words of their lords, and were willing to depart and follow Oromë; and these were known ever after as the Eldar, by the name that Oromë gave to the Elves in the beginning, in their own tongue. But many refused the summons, preferring the starlight and the wide spaces of Middle-earth to the rumour of the Trees; and these are the Avari, the Unwilling, and they were sundered in that time from the Eldar, and met never again until many ages were past.
The Silmarillion III Quenta Silmarillion Chapter 3: "Of the Coming of the Elves and the Captivity of Melkor"
This split occurred in YT 1105, about 11 000 years before the events of The Lord of the Rings.
The Nandor Of those Elves who chose to go to Aman (who, collectively, are called the Eldar), some of them stopped at the Misty Mountains in YT 1115 and went no further; these are the Nandor (emphasis mine):
This river, it is said, was even the river which was after called Anduin the Great, and was ever the frontier of the west-lands of Middle-earth. But the mountains were the Hithaeglir, the Towers of Mist upon the borders of Eriador; yet they were taller and more terrible in those days, and were reared by Melkor to hinder the riding of Oromë. Now the Teleri abode long on the east bank of that river and wished to remain there, but the Vanyar and me Noldor passed over it, and Oromë led them into the passes of the mountains. And when Oromë was gone forward the Teleri looked upon the shadowy heights and were afraid.
Then one arose in the host of Olwë, which was ever the hindmost on the road; Lenwë he was called. He forsook the westward march, and led away a numerous people, southwards down the great river, and they passed out of the knowledge of their kin until long years were past. Those were the Nandor; and they became a people apart, unlike their kin, save that they loved water, and dwelt most beside falls and running streams. Greater knowledge they had of living things, tree and herb, bird and beast, than all other Elves. In after years Denethor, son of Lenwë, turned again west at last, and led a part of that people over the mountains into Beleriand ere the rising of the Moon.
The Silmarillion III Quenta Silmarillion Chapter 3: "Of the Coming of the Elves and the Captivity of Melkor"
But we don't usually talk about the Nandor; usually we talk about one of the two groups they later divided into:
The Laiquendi (Green-elves) The Nandor eventually subdivided further, in YT 1350 when some of them crossed the Misty Mountains, came into Ossiriand, and became the Green-elves:
These names were however later replaced among the Sindar by the 'Green-elves', at least as far as the inhabitants of Ossiriand were concerned, for they withdrew themselves and took as little part in the strife with Morgoth as they could. This name, [singular] Laegel, [plural] Laegil, class-plural Laegrim or Laegel(d)rim, was given both because of the greeness of the land of Lindon, and because the Laegrim clothed themselves in green as an aid to secrecy. This term the Noldor translated into Quenya Laiquendi; but it was not much used.
History of Middle-earth XI The War of the Jewels Chapter 4: Quendi and Eldar Part C "The Clan-names, with notes on other names for divisions of the Eldar
The Silvan (Wood-elves) The Nandor who chose not to cross into Beleriand became known as the Silvan. These are the Wood-Elves referred to in The Hobbit, as well as most residents of Lothlórien:
The Silvan Elves (Tawarwaith) were in origin Teleri, and so remoter kin of the Sindar, though even longer separated from them than the Teleri of Valinor. They were descended from those of the Teleri who, on the Great Journey, were daunted by the Misty Mountains and lingered in the Vale of Anduin, and so never reached Beleriand or the Sea. They were thus closer akin to the Nandor (otherwise called the Green-elves) of Ossiriand, who eventually crossed the mountains and came at last into Beleriand.
Unfinished Tales Part 2: "The Second Age" Appendix A The Silvan Elves and their Speech
The Sindar (Grey-elves) The final major sundering occurred in YT 1132, when one of the Elven kings, Elwë, became lost and his people stayed behind to look for him. Elwë would later return (and be renamed Elu Thingol) and his people came to be known as the Sindar:
[Sindar] was the name given by the Exiled Noldor to the second largest of the divisions of the Eldar. It was applied to all the Elves of Telerin origin that the Noldor found in Beleriand, though it later excluded the Nandor, except those who were the direct subjects of Elwë, or had become merged with his people. The name meant 'the Grey', or 'the Grey-elves'
History of Middle-earth XI The War of the Jewels Chapter 4: Quendi and Eldar Part C "The Clan-names, with notes on other names for divisions of the Eldar
Legolas and Thranduil are technically Sindar, although they've "gone native", as it were.
Although these splits occurred a rather long time ago, in human terms, with Elvish reproduction there hasn't been enough time for significant evolution; the longest chain of ancestry I can find is Arwen's, which connects us to YT 1050 in only six generations3, not enough time to speciate.
1 Strictly speaking, Elves and Men are the same species
2 The term "Dark-elf" isn't used entirely consistently in Tolkien's writings; in some contexts it refers to the Moriquendi, those Elves who didn't behold the Light of the Two Trees of Aman (a group which includes the Nandor and most of the Sindar4), but in some it refers exclusively to the Avari. It's also not to be confused with the epithet "Dark Elf", applied to Eöl
3 With thanks from LOTRProject.com: Finwë -> Fingolfin -> Turgon -> Idril -> Eärendil -> Elrond -> Arwen
Or if you don't like that one, with Eärendil being Half-elven and all: Elmo (yes, really) -> Galadhon -> Galathil -> Nimloth -> Elwing -> Elrond -> Arwen
4 Thingol is generally not counted among the Moriquendi, because he had visited Aman before the Great Journey even began, with the intent that he help convince the other Elves to come
They are all a single "species", in the sense that they were all created at the same time and are the same kind of being. Over time, they've split off into various communities, depending on where they lived, who they chose to rule over them, etc. The entire family tree of the Elves is rather complex:
The three "clans" of Elves that eventually came to Middle-earth were the Vanyar, the Noldor, and the Teleri, though the Vanyar had largely left long before the time of the novels. The Elves of Rivendell (Elrond and his clan) were of Noldor descent, while the ones in Lothlorien (the "wood elves") were primarily Telerin. The only trace of the Vanyar we see (as far as I can recall) is that Galadriel was descended from one of the leaders of the Vanyar.
Since they tended to live in isolation, the different "clans" of Elves developed their own behaviors and tendencies. For example, the "wood elves" of Mirkwood (like Legolas and his father) were descended from the same ancestors as the elves of Lothlorien, but they behaves very differently.
"Species" isn't the right word here; nor would "race" be, really. Maybe "breed" comes near the mark.
All the Elves are descended from the same folk that awoke in Cuiviénen in the earliest days of the First Age, well before the rising of the Sun. They dwelt there for many years before being discovered by Oromë, one of the Ainur (gods/angels), who summoned them to Aman. Many agreed, and became Eldar, the High Elves; the others who refused were called Avari, unwilling. Not all the Eldar arrived in Aman - the Sindar turned back before crossing the Great Sea - and even some of those that did, the Noldor (among them Galadriel), later rebelled and returned to Middle-Earth. But nevertheless the Eldar as a group were still considered nobler than the Avari.
The Avari themselves remained in Middle-Earth and spread all over. At the time of the War of the Rings, the elven countries - Lothlórien, northern Mirkwood, Rivendell - were ruled by Eldar but mainly peopled by Avari. The Wood-Elves were one of these groups of Avari.
All of the Elves in the Tolkien Legendarium are descended from those that awoke at Cuivienen and are referred to as the Quendi. They are all the same species. The different names just refer to different groupings of Elves.
There were initially three groups of Elves:
the Minyar, most of whom went to Valinor with Ingwe, and became the Vanyar
the Tatyar, half of whom went to Valinor with Finwe, and became the Noldor
the Lindar/Nelyar, some of whom went to Valinor (Tol Eressa) and who were initially led by Elwe/Thingol and Olwe. Thingol stayed behind in Middle-Earth with Melian and formed Doriath, and many of his group stayed with him. Olwe led the rest to Tol Eressa and they became the Falmari. All of the Lindar/Nelyar are also referred to as the Teleri.
Beyond this, the first distinction that occurs is between those that initially followed Orome to Valinor (the Eldar) and those that stayed behind at Cuivienen (the Avari). Note that some of the Avari did eventually expand westward into Beleriand after a while.
Along the way, some of the Eldar stopped following Orome and became the Umanyar. They were split up between (what would become):
the Sindar (Grey Elves), which included the Falathrim (Sea Elves) and the Eglath (those that followed Thingol)
the Nandor (the Wood Elves), which included the Laiquendi (Green Elves) and the Silvan Elves.
The Avari and the Umanyar together are referred to as the Moriquendi.
Of the Eldar that followed Orome all the way to Valinor, they were split into the Vanyar, the Noldor, and the Falmari (a group of the Teleri).
Later on, some of the Noldor returned to Middle-Earth with Feanor.
