Inverse time lag relays in protection
The way I read it, the definite time lag gives a constant delay from the time some minimum current is applied to the time the relay is activated.  That way you can, for instance, sequence events triggered by the same activation.  The inverse definite minimum will do that too, but additionally gives you the option to extend that time by applying a current lower than the minimum for the guaranteed delay.  That guarantees it won't happen too quickly, but at the same time allows additional control based on immediate circumstances.