The hungry and the frightened seek combat and conquest, hence vijay—victory where someone is defeated. The wise seek a different kind of victory, jai—where no one is defeated, where the self is able to conquer its own hunger and fear to acknowledge, appreciate, even accommodate the other. Both jai and vijay seem to mean the same thing, ‘hail’ or ‘victory’, but there is a nuance in the meaning, the preference for internal victory in the case of jai over external victory in the case of vijay. This jai is what we want for Hanuman, and from Hanuman, as we read the Hanuman Chalisa.
