Not 100% since I'm not Norwegian, but if it's the same difference as in Dutch, "ild" will be the phenomenon/element of fire, useful fire, or fire in general, (e.g. the pan is heated by the fire) while "brann" is uncontrolled, dangerous or damaging fire (e.g. there was a fire downtown).
ild is the element fire, or it can be flame. brann is uncontrolled or accidental fire, it could be oil in a pan or a house, or a forest fire.
Norwegian has many words for fire: fyr, bål, ild, brann, forbrenning... And even more, if you speak of lighting it!