The change between hangover and withdrawal is when I noticed my body and brain had shifted in the processing of alcohol.
Hangover focuses on expelling the poison, whereas the withdrawal process is your body sending signals of a new physiological need for a substance, despite obvious signs that it's a toxin...and to go along with that, your brain and neurotransmitters have essentially rewired themselves to rely upon it.
It takes different quantities over different spans of time for all of us, but I would gather we all end up near the same spot of feeling like hell and noticing that something is very very wrong.