What's the difference between "apparel" and "clothing"?

Those two words seems referring to one thing.

"Apparel" can also include things like nametags, jewelry or other stuff you wear. "Clothing" tends to refer to stuff traditionally made from cloth (but still includes synthetic variants.)

The specific dividing line between the two terms is subjective and will differ from person to person. "Apparel" is also slightly more formal.

I would rather use apparel when the outfit is complex or fancy. It is closer to attire than to dress.

The origin is from Old French appareil which has a connotation of lengthy or complex preparation. You used it for a ship being prepared for taking the sea or a fighter being equipped for fighting.
These two senses once existed also in English but they are now lost I believe.