Much of the rules and mechanisms of a role-playing game are based on the "common" vernacular, without explicitly specifying a definition or in-game mechanics. If all else fails, consult a dictionary if you need a specific word-wise scheme for these difficult players or DMs.
Usually, you consider things in your player inventory as worn or worn. Even if you do not know they are there. If you carry a box of nicks, it is also assumed that you carry everything in this box. If you really want to choose it, "wear" earrings in your earlobes and nose rings in your septum. In that case, you might argue that you "carry" an arrowhead in your skull.
You can either cast "light" or "darkness" on an object and then lay it on a character without any problems. The worn or worn object can not come from another inventory (if I understand the question / application correctly).
In the case of a "Darkness" arrow, is the entire arrow in the enemy? Does the spell influence the entire arrow on the arrowhead only? Or only the springs? If you make a selection at this level, it always ends up discriminating against the DM.