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When Dexter Drake gets a random spell after casting one, he GAINS that spell. Correct?
When Preston Fairmont gets an item after a trade action, he GAINS that item. Correct?
Thinking about their spec abilities
New South Wales
Dexter definitely gains a new Spell when he casts one. The rules quite clearly tell you to Gain the new Spell card.
Items are a weird one. The rules don't use the term 'gain' when you pick up or trade items. It also feels wrong that this would be the case, as Preston could always use a Trade Action to just drop an item he is holding and pick it up again to trigger his ability. That seems too easy.
So yes, you gain a new Sell when you cast it, but no, you do not gain a new Item when you trade it or pick it up, it must be gifted from the deck for Preston to use his ability.
Having said that, I see no problem with allowing an investigator to gain an item that was never held by investigators (because it was seeded in a room by the app). It's probably a house rule, but it seems like these types of Items would be intended to trigger Preston's ability.