Well, I'm not sure whether my homebrew elves qualify regarding the wording of the question, but anyway, here you go

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First thing to put upfront is that they generally encompass the whole elf/dwarf/gnome/halfling slot of standard D&D. Second thing is that they borrow a bit from old mythology and also Tolkien, but in the way they were portrayed in 'The Hobbit': having their dwellings underground and being creatures of twilight. There are basically 5 cultural groups (I take generic names instead of the country names I gave them):
High elves: I have nothing to add to Gez's excellent description

! They are nearly extinct, though, because they were almost completely destroyed in a great war, where they wanted to eliminate human presence on the central continent of my campaign. None of the other elf groups helped them. The survivors have one city behind a swamp on the western coast left, brood in their dream of former glory, of revenge and their detestation for all other races, and they terrorize a small group of former wood elven underlings who made the error to believe in the high elves' superiority.
'Wood elves': Think Tolkien's 'King under the Mountain'. They live in underground dwellings in the woods and grow special food plants in mixed plantations under the trees, and these plantations are hardly recognizable as such by untrained human eyes. They fare quite well with their human neighbours because of some time in history where they had to work together in order to achieve a common goal.
'Hill elves': They live under the almost bare hills of the south in small communities that are often connected by underground canals. They hunt and gather plants on the surface during the night. They are in a constant war with the human lands that claim the same area, but this war is highly ritualized by now, as long as it is already going on. On a certain religious holiday, human pilgrims throw lots of alchemist fire and similar burning stuff into putative elven dens. The elves reward them with illusions of screams of death and use the day to burn their 'holiday ceramic' in those pits. Of course, higher human priests know this, but they keep the tradition up, nevertheless.
'Dark elves': They live under the highest mountains in the center of the continent in caves at lakes and an underground stream that has its origin in a high, open but inaccessible lake up in the mountains. They live mostly on fish and fungi and don't have much contact with other races, including elves, except the 'hill elves', who extended their canal system to that mountain lake. The 'dark elves' have a relatively advanced culture and like to breed monsters, including a slave race. They are not evil, just different.
'Fire elves': The live under the snow-capped, fire-spitting volcanoes of the frozen north. They are excellent smiths. For food, they go hunting, fishing or collecting seaweed during the night. They are reclusive, but trade with others for plants and wood.
Again, these are less racial than cultural distinctions. Think of people of different countries. I also have some fey element in those cultures, as elves who want to prolong their life and commit themselves to protecting their family or clan can perform a ritual that turns them to a fey creature. This comes with a price, though, as they will forget their former lives and friends after some while, finally passing over into the shadows.