I've always thought the numbering system was a cool piece of nostalgic junkie trivia. I believe it actually came from one of the big heroin manufacturing operations in SouthEast Asia in the 'Golden Triangle', as a way for them to label their product. I'd also heard that it was a way for the DEA to categorize junk coming into the US from Asia during the Vietnam War era.
I always thought that it went like this:
#1 Morphine powder
#2 Raw, relatively impure heroin freebase
#3 Heroin freebase
#4 Heroin hydrochloride salt
On the East Cost of the US, #4 is what you're going to mainly come into contact with, with a little bit of black tar showing up now and then. Black tar kind of blows away the numbering system as it's crude way of manufacture means it contains a bit of everything.
'China white' always meant 'white', pure, #4 powder and we usually referred to the good stuff as 'China white' in the mid-90s or so. I believe the reference originally meant that it was of Asian origin and white in color. Back in the day, the stuff from Asia was usually the best.
Over the years I did hear the reference shift to either fentanyl laced heroin, or just fentanyl. Not sure how that happened.