The distinction in my humble opinion is this.
Not giving a shit, "I don't care about this bullshit".
I have no fucks left to give, "I care or at least I used to, but I am too burnt out to give a fuck anymore".
> Not having fucks left to give is when you stop caring what others think.
> Not giving a shit is when you stop caring.
Burnout? Sounds fair. However, there's a point beyond burnout, IMO, when failure is not an option, where you exceed your capacity and limitations and are no longer tethered or limited by feelings of exhaustion. Then, the question is: why should I care? For what should I care about?