What do elemental icons next to enemy names mean?

When fighting an opponent, sometimes there will be an elemental icon to the right of an enemy’s name.

I suspect this indicates either an elemental weakness or resistance, but I’m not sure which.

What does it mean when an enemy has an elemental icon next to their name?

Solution 1:

You’re right in that this indicates an elemental weakness. Special moves (A button moves) and Chain Attacks (since they use Special moves) of the right element deal increased damage to these enemies. Blade Arts (X, Y, B moves) won’t deal increased damage.

The element shown is the element they're weak against.