Yes, the Norse alfar are fates, and the alf women are explicitly nornir. But all elves are forces of fate, in the British traditions too. Because both are "fates" and both are superhumanly beautiful, are why Brits merged the Norse alfar and the Celtic sidhe (sith, shee).
The word "Fey" means fate.
[Lat. fatum "fate" > fata "a decider of fate, a fate, a norn" > OF. faie, feie > E. fay, Fey. Related to ME. faie -erie, faierie, feierie, faerie, fairie, fairy, of various spellings "the realm of fey, the activity of fey", whence the original term for "magic"]
Elves are prescients who foretell the future, speaking magic to alter and navigate the future. They are fateful magic manifesting a human shape.
Elves are nonhuman forces of sunlight, fate, and magic. But they entangle human fates, including birth, blessings, sexuality, love, children, success, and time of honorable death. Whence they adopt human forms. All of this fate-fey activity is magic, speaking words to foretell and alter reality.
The British elves are more about fertile soil rather than sunlight, because of the sidhe merger, but the rest of the concept is roughly the same.