The difference between Damaged and Faulty

When used as adjectives, damaged means suffered a damage, whereas faulty means having or displaying faults.

check bellow for the other definitions of Damaged and Faulty

Faulty as an adjective:

Having or displaying faults; not perfect; not adequate or acceptable.

Examples:

"They replaced the faulty wiring and it has worked fine ever since."

"I don't think you can infer that from the premise. It's a faulty argument."
Faulty as an adjective (obsolete):

At fault, to blame; guilty.