The Wood Elves are Druids and Rangers, mages and gishes: "a magic people". "Holding high a gnarled staff wreathed with holly, a [wood] elf summons the fury of the storm and calls down lightning to smite [those] who threaten her forest."
These "mortals" spend their centuries personally mastering magic.
Elves have magic rituals that are mainly unique to elves, such as High culture, for shaping treehouse towns from living wood.
In my campaign, the Faerie are exclusively fullcasters without gishes. In 4e, part of my flavor for the Feywild is, the martial power source doesnt exist. The martial power source is strictly a Material Plane source. The Fey magical power source is especially psionic, arcane, and primal, but not necromancy which is a Shadowfell thing.
Nevertheless, the Players Handbook makes clear the Elf are magical, including Fey ancestry for every Elf, High cantrip and Uda innate spells.
A "nonmagical elf" is an oxymoron, and would simply be a human.