"Carnauba wax, son. Nothing else in the world smells like that. I love the smell of carnauba in the morning. You know, one time we had a car washed, polished and waxed over 12 hours. When it was all over, I walked up. We didn't find one of 'em, not one stinkin' raindrop actually touching the paint. The smell, you know that carnauba smell? The whole car. Smelled like... victory. Someday this detailing war's gonna end."
Lieutenant Colonel Bill Kilgore (1979)
The phrase detailing is used to separate us from car wash and hand wash's.
They are both washing a car however a detailer will take more care and pay attention to the details which in effect takes more time.
For example a hand car wash will have you car washed in 30min, for me to wash (detail) that car will take approx 5-7 hours
Clay as you mentioned is just part of the detail process just before machine polish or compounding