I purchase a truck with sticker of $20k and trade in a fully depreciated truck which I get $2k towards the new one. Do I record the new truck at $20k and recognize the gain or simply apply the $2k toward the new truck and record it at $18k? (US GAAP)

The new truck should be recorded at $18K. No gain is recorded because in an exchange transaction, gains on similar assets are deferred.

Trading a truck with a 2K value for a new truck is not a like exchange.

Also the 2K isn't a gain unless it had no salvage. (Fully depreciated doesn't mean it has no value, only that you've depreciated everything you're going to.) But if we assume that 2K really is a gain, take the gain.

The other question is why you're paying sticker and what kind of truck is that cheap? Which makes me wonder - is this homework? If so, and you're in principles, the book might be behind the times and still teaching that this is a "like-exchange" even though it's not.