On the wiki it states that "damage taken from fire status can only be reduced by fire-resistant armor. Once alight, a player cannot avoid the damage, even if blocking, until it wears off".
So what does the Fire resist buff on my Owl Shield do? And if it does help, can it stack with fire resist armor?
The resistances on your shield only apply when you're shielded. Shields, like you, have a health (represented by the heart bar you see when you mouse over the shield in your inventory). That health can be drained by damage, in a manner similar to you. So a shield that has no defense against elemental damage will take the full brunt of such an attack, but a shield that has some will mitigate some of that damage. (This is why a lot of people go with an Owlite shield; the high normal and elemental defense are valuable in Tier 2 and Tier 3, where non-normal damage plays a heavier role).
A shield with a status resistance will resist that status effect taking place while you're shielding. So if you have fire and elemental resistance, if you shield, you could stand between two flamethrower puppies for quite some time before the shield breaks.
Armor, on the other hand, works on you directly and affects your stats at all times. Armor stats work in a way similar to shield stats.
Hope this helps.
I believe the resistances on your shield apply all the time, while the defenses and health of your are separate from the defenses of your armor and only apply when you are shielding. I'm not totally sure, wish I could be more help. Sort of sad topics like this get ignored while people constantly bump numerous topics bawwing about energy costs.