The thing about the elves that most modern depictions descend from is that they're in a peculiar point in their history. The Tolkien Elves in their height ran the mortal plane of the setting. They lived lives, had normal families, all sorts of things you expect from humans. They just lived on grander scales, as did everything in their era. The Elves of the LotR are a passing race. Most have moved on to notHeaven, and those that remain are specifically charged with safeguarding the world and usually have a particular sin or past folly they must overcome and make up for. By the end of the LotR, their last mission has ended and most are moving on as well.
It's very unlike most depictions of elves in any setting, really. The reason is as it often is, the shallow mimicry of an execution of a concept without the guiding principles and context of it. The Elves are leaving as part of a larger symbolism of the passing of an age. Gone are the days of fighting dragons bigger than mountain ranges, stealing light from trees, and slaying the fallen angels of the devils. Now comes the mundane age of recorded history. So the elves, immortal and super human, crafted for a different age, pass on too and their magical influence on the world wanes. It's all very poetic and so on.
Most just take the "immortal/live long, magic, tree fuckers, bows and arrows, not many of them" thing and run with that.