Worn and Worn-down

Worn adjective - Depleted in strength, energy, or freshness.

Worn-down and worn are semantically related in used topic. In some cases you can use "Worn-down" instead an adjective "Worn".

Worn and worn-down are semantically related in exhausted topic. You can use "Worn" instead an adjective phrase "Worn-down", if it concerns topics such as haggard.