What's the difference between "operating voltage" and "input voltage"?

Hi, and welcome to the forum.
Hope this helps.

The 5volt regulator on the Uno needs at least 1volt more on it's input to make a stable 5volt.
So minimum voltage on the V-in pin is 6volt.

There is an onboard mosfet that switches off USB power when the Arduino is powered externally.
That switch point is set to 6.6volt.
So minimum voltage on V-in for USB power to disconnect is 6.6volt.

There is a reverse protection diode between the DC socket and V-in with a volt drop of ~0.7volt.
When you power the Uno on the DC socket, you have to add 0.7volt to the above statements.

Upper voltage limit could depend on the regulator's input limit (usually 20volt), or the smoothing caps (16volt on an Uno clone).
At those voltages you can't draw any current from the 5volt or 3.3volt pin (for LEDs/sensors).
With 12volt on V-in, current draw for sensors is ~100mA max.
With 6volt on V-in, that increases to ~700mA.
Leo..