Difference of inductor rated current based on "Inductance change" vs based "Temperature rise"?
The inductance decreases because of either current or temperature.

Higher currents cause the magnetic material to saturate (lose permeability). This occurs at (nearly) any temperature.

High temperatures also cause the material to lose permeability. Temperatures are raised by I^2.R losses in the wiring as well as core losses in the magnetic material.