The current rating can be applied at a constant rate without thermal damage. This is a safe rule of thumb but a current above the ‘current rating’ can be achieved when considering carefully the time and temperature rise. The saturation current is where the Inductance drops to a specified level in the datasheet.
We can look at part number 541-1086-1-ND as an example. 680nH 10A current rating with 15A saturation current.
Note (1) At the rated 10A we can see the L inductance will be .680uH at 40°C. As the current increases we can see from the graph the L inductance decreases. Note (2) in their specs at saturation current the inductance has decreased by 20% of the nominal rating of .680uH.
