RAW - No, Otto's Irresistible Dance is not a Charm spell
It does not say that the target will be "charmed", and the condition it imposes is significantly different than the description of the "Charmed" condition.
OID:
A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it.
Charmed:
A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects. The charmer has advantage on any ability check to interact socially with the creature.
A dancing creature can attack the caster (with disadvantage -- and that disadvantage applies to any attack, not just against the caster) and can cast AoE spells that include the caster and anyone else they choose in the target area with no penalty. They just can't move freely. A charmed character can move freely but can't attack or target the caster.
Furthermore, if it were a Charm spell, it would not be necessary to specify that "[c]reatures that can't be charmed are immune to this spell." That appears to be listed as a special exception.
RAI - No, Otto's Irresistible Dance does not impose the Charmed condition
Jeremy Crawford has tweeted saying:
Being charmed means being subjected to the charmed condition
Since OID does not impose the Charmed condition, the Fey Ancestry resistance to "being charmed" does not apply.
What makes sense?
Webster's dictionary says:
charm: to affect by or as if by magic : compel
Magically forcing someone to dance seems to fall completely within that definition.
I would give those with Fey Ancestry advantage on saves against all enchantment spells that compel the user to do something that is not their own free choice. This includes many spells that do not specifically say they are "charms" or that they impose the "Charmed" condition, such as command, compelled duel, and yes, Otto's irresistible dance. I believe those all fall within the common sense and dictionary definitions of "charmed" in this context, and there's nothing in the description of Fey Ancestry that says it only applies to things that grant the "Charmed" condition.
Only a game feature (such as a class feature or race feature) that specifically grants advantage against madness, or grants advantage on saving throws against magical effects, assuming the source of the madness is magical (which isn't always the case). For example:
- The Robe of the Archmagi and the Spellguard shield grant advantage on saving throws against spells and magical effect.
- A gnome's Gnome Cunning racial feature allows advantage on Int, Wis, and Cha saving throws against magic
- A monk's diamond soul class feature allows the monk to spend 1 ki point to re-roll a failed saving throw, which isn't advantage, but has an effect very similar to advantage.
- The Wizard's school of abjuration Spell Resistance feature might help if the source of the madness is specifically a spell (which is unlikely)
- Finally, there's inspiration which grants advantage on any d20 roll.
Hope this helps.
Best Answer
Charmed is a specific game condition. From Appendix A of the PHB (page 290):
So Fey Ancestry gives advantage on any saving throw to avoid receiving the Charmed condition. Or to put it differently, a creature with Fey Ancestry has advantage on any saving throw made to avoid the effect of a spell, trap, or other effect that inflicts the Charmed condition.