No, they did not originate from humans.
Warcraft: Chronicle, Vol. 1 tells the tale of most of the species origins on Azeroth.
While there were a great many diverse races in the very early days of what we would call Azeroth (after the Titans were done chilling out the place), trolls were the most dominant. One particular clan was known as dark trolls, known for being nocturnal and more peaceful than others (trolls are known throughout history for their violence). This clan settled in the area around the Well of Eternity. The immense power in the well got slowly absorbed by the dark trolls and altered them. Their minds grew quicker, their form less hunched. Eventually, other than pointy ears and skin tone, they barely resembled trolls at all. They became the first night elves. Their immense power also stems from the Well, giving them both an innate talent for channeling magic due to how it altered them, and a giant source of it to wield against their enemies.
While night elves later had a few disasters (understatement) that led to the offshoot elven races, and led night elves to seek natural power rather than magic power, humans aren't in any way related to them. Humans are descended from Vrykul, the giants of the north, who in turn were descended from the original stone and metal Titan creations and servants. A degenerative Curse of Flesh first transformed the titan servants from elementals to flesh and blood creatures, creating the Vrykul, then that curse evolved and hit them again, making them give birth to "weakling runts". Said runts were the first humans, and enough of them were exiled to safety to start their own civilization in what would later be called Tirisfal. Dwarves and Gnomes have a similar origin story, also being descended from Titan creations, so those would be the closest kin to humans under the current history.