Resist Fire will reduce the damage from Fire attacks. So if you have a 100 point fire ball thrown at you and you have 40 Resist Fire, the fireball will be reduced to 60 points. But if someone hits you a 100 point warhammer then that damage will be not be reduced by Resist Fire
Fire Shield will both reduce the damage from Fire attacks and add to your armor rating. So if you have a 100 point fire ball thrown at you and you have 40 Fire Shield, the fireball will be reduced to 60 points. If someone hits you a 100 point warhammer then that damage will be reduced to 60 points by the Fire Shield.
Resist Fire and Fire Shield are calculated separately. So with 50 points Fire Shield and 50 points Fire Resist, a 100 point fireball will be reduced to 25 points.
The Armor Rating from a Fire Shield will add with other Armor ratings. So if you have 30 points of Armor and then add 10 points of Fire Shield, you will have 40 points of armor. And a 100 point warhammer will be reduced to 60 points.