Up is more “what’s up”, and down is more I acknowledge your presence and show you no disrespect.
Chin down is more respectful, more like saying “Hello”. Chin up is more informal, and more like saying “what up?” Depends on the audience. I’d probably never start a job interview with a chin up head nod. But i’d greet my buddies with one.
In addition to what you said, I also see downward as indicating that the greeting is over, there is 0% chance that I want to interact further. With upward there is maybe a 3% chance that we’ll actually stop to talk.
This is an example of the type of thing no one explicitly tells you but everyone picks up if they’ve been around enough.