Is the 1st level Command spell [PHB p223] a "charm" (that would trigger an elf's Fey Ancestry [PHB p23] racial ability and thus get advantage on the saving throw)?
No, Command isn't a charm and wouldn't trigger Fey Ancestry.
Spells themselves aren't classified as charms under any technical game term. They are categorized by the eight schools of magic found on page 203 of the PHB.
Fey Ancestry and (almost) anything that mentions being Charmed is referring to the charmed condition found on page 290 of the PHB.
As such, Fey Ancestry would only come into effect when a spell specifically mentions that its target is being charmed, thus imposing the Charmed condition.
An example of such a spell would be Dominate Person:
You attempt to beguile a humanoid that you can see within range. It must succeed on a Wisdom saving throw or be charmed by you for the duration. (PHB pg.235)
Whereas Command doesn't mention anything about the target being charmed, it just says:
The target must succeed on a Wisdom saving throw or follow the command on its next turn.