Normal aviation nominclature.
Turbocharge Gas driven.
Supercharge Mechanicly driven.
Capt. But I do agree on you technical definition.
And turbochargers I belive can also effected by rpm.
Basicly the turbo will spin based on the volumn of gas (not fuel) exiting the engine. More Throttle, more expansion, more gas more turbo rpm.
Like you state.
But also, Same gas per stroke, higher RPM,more gas leaving cylinder hence more turbo rpm.
Now some of the planes we have also had a turbo rpm control to not over speed the turbo. Basicly a type of waste gate before the turbo.
HiTech