You're kidding right? Amperage goes up with load. Amperage IS load.
Where
capacity is limited, no load voltage will always be higher than loaded
voltage.

Capacity is always limited. Voltage only stays constant with load with
voltage regulated supplies that are not loaded to capacity.

To "load" something means to increase the current flowing through it.
Amperage does indeed go up with load (usually).

Put a volt meter across your 12V car battery. If it reads 12V, your battery
is "dead" and probably won't start the engine. An open circuit car battery
in good condition that hasn't been recently charged will have ~12.6 V.
across the terminals.