“wear off” is used for things that are applied topically: "The paint was worn off the top of the hand rail." "Cheap nail polish wears off quickly.” “This suncreen will wear off after only 1 hour in the water, so re-apply frequently.” “The letters on my kyboard are worn off, but the keys themselves aren’t worn out yet." Or for the effect of something that someone has been exposed to (a drug or chemical): "The effects of mustard gas don’t wear off. If the victims survive the attack, the effects of the gas will last for the rest of their lives.” “The drug wears off after 3 hours, so you will be able to drive home yourself.” “wear out” is not acceptable in those circumstances. “wear out “ is used when something is not usable anymore: clothes, cars computers, books, stoves, etc: "This book is worn out. The print is so worn off I can’t read it anymore.” “My hip is worn out, I can barely walk." Or when people are tired or exhausted physically or emotionally: “I’m worn out from scrubbing the floor all day.” “Going through that divorce really wore him out."

Wear out basically mean something has been overused. It can be anything. A car, clothes, people, a pen etc etc. Wear off is not something that i can think of being used other than when someone might say to someone who is too drunk 'The alcohol will wear off soon' or some medication will 'wear off' after a while.

to wear off = to come off of a outside surface, such as paint or makeup; the expiration of a magic spell to wear out = to degrade over time to the point where it breaks; to tire out. My make-up wore off while I was sleeping. The paint has worn off due to wind erosion over the years. The love potion has worn off. He doesn't love me any more. That car is worn out. It won't run any more. These clothes are old and worn out. They are almost thread-bare. I am worn out (exhausted). I need to rest. I can't continue.