The rules don't strictly adjudicate this.
In my opinion, it seems the intent is that worn/carried objects are things you have "equipped" or are in your bags/packs. It would seem the intent was to simplify combat with respect to spells that would otherwise incinerate all of a character's possessions.
Objects, which includes items, have only two inherent immunities: Poison and Psychic. There is a table in the DMG pp 249-250 which details item types AC values as well as recommended hit points based on size.
As 5e is about rulings over rules, it would seem that common sense should dictate a rational course of action with respect to adjudicating these kinds of questions. The rules won't address things like, "Well does it say the sword is made out of iron?" It's assumed that a weapon is made up of it's common components unless otherwise stated. Much the same as an object is assumed to be what it is unless specified as something other. So the difference between the rope binding me to a tree, and the rope in my backpack is that the rope binding me to a tree would be burned away if I ignited it, and the one in my backpack would remain unhindered.
Unless of course you kicked my backpack into the fire when I set it down. Then it would ignite. I know it seems paradoxical, but the intent seems to be to avoid a Wizard losing their spellbook, robes and staff every single encounter due to a lousy fireball.