If I purchase merchandise in a physical store, and then (accidentally or not) leave the merchandise at the store after I've paid for it, is the store allowed to resell that merchandise to another customer?
How does this scenario differ from leaving personal items at the store that I purchased elsewhere?
If the common law applies (i.e. there is no statute that changes it) then it depends on if the item was lost, mislaid or abandoned. The US has statute law dealing with lost money but that is not the question here.
Property is generally deemed to have been lost if it is found in a place where the true owner likely did not intend to set it down, and where it is not likely to be found by the true owner. At common law, the finder of a lost item could claim the right to possess the item against any person except the true owner or any previous possessors.
Property is generally deemed to have been mislaid or misplaced if it is found in a place where the true owner likely did intend to set it, but then simply forgot to pick it up again. For example, a wallet found in a shop lying on a counter near a cash register will likely be deemed misplaced rather than lost. Under common law principles, the finder of a misplaced object has a duty to turn it over to the owner of the premises, on the theory that the true owner is likely to return to that location to search for his misplaced item. If the true owner does not return within a reasonable time (which varies considerably depending on the circumstances), the property becomes that of the owner of the premises.
Property is generally deemed to have been abandoned if it is found in a place where the true owner likely intended to leave it, but is in such a condition that it is apparent that he or she has no intention of returning to claim it. Abandoned property generally becomes the property of whoever should find it and take possession of it first, although some states have enacted statutes under which certain kinds of abandoned property – usually cars, wrecked ships and wrecked aircraft – escheat, meaning that they become the property of the state.
For your specifics:
If I purchase merchandise in a physical store, and then (accidentally or not) leave the merchandise at the store after I've paid for it, is the store allowed to resell that merchandise to another customer?
This would be mislaid property and if they cannot find you and you do not return to claim it after a reasonable time (which would be different for a Mars bar and a Boeing 747) then it is theirs and they can do what they want with it: including sell it to someone else.
How does this scenario differ from leaving personal items at the store that I purchased elsewhere?
It doesn't.
Uniform Commercial Code § 2-403(2)-(3), enacted in every U.S. jurisdiction, provides that:
(2) Any entrusting of possession of goods to a merchant who deals in goods of that kind gives him power to transfer all rights of the entruster to a buyer in ordinary course of business.
(3) "Entrusting" includes any delivery and any acquiescence in retention of possession regardless of any condition expressed between the parties to the delivery or acquiescence and regardless of whether the procurement of the entrusting or the possessor's disposition of the goods have been such as to be larcenous under the criminal law.
So, if the store sold the merchandise you left in the store in the original question, the subsequent buyer of the goods would have good title to the goods as a bona fide purchaser for value.
Therefore, you would have to resort to some other remedy than regaining possession of the originally purchased merchandise from the store, such as receiving a replacement items or a refund of the purchase price (possibly with an adjustment for change in the item's market value between the time it was purchased and the time you received a substitute item). See generally, Uniform Commercial Code Article 2, §§ 711, 713 and 715.
Arguably, since the sale is complete, you avail yourself not of UCC remedies after the store has conveyed good title to a third-party, but of a tort lawsuit for conversion, in which case the issue is, as noted in the other answer by @DaleM, whether there was abandonment of the goods (which seems unlikely in most cases contemplated by the question).
If the goods were not abandoned than your remedy would be to sue the store for the fair market value of the items sold to a third-party (although normally, the purchase price would be a conclusive proof of this value in a short time frame from a consumer good).
How does this scenario differ from leaving personal items at the store that I purchased elsewhere?
Somewhat. A store cannot convey good title to a third-party in personal items of a type that it does not sell. So you could bring an action for replevin to recover the personal item you left behind from a third-party to whom the merchant sold it, for example, if you left behind at pocket watch with a car dealer (leaving the buyer of the pocket watch with a claim against the car dealer for an implied in law breach of warranty of title in connection with a sale of goods), but not if you left behind a pocket watch at a pawn shop.
