The vocabulary is doing real work, so it is worth five words. The originator is the person paying. A payment order is the instruction. The originator's bank issues or receives that first order, an intermediary bank may sit in the middle, and the beneficiary's bank holds the account being credited. 4A-104(a) then supplies the fact everything else hangs on: "A funds transfer is completed by acceptance by the beneficiary's bank of a payment order for the benefit of the beneficiary of the originator's payment order." Completion is an event at the far end of the chain, not at the moment you clicked send.
Why a wire you sent is treated as yours, stated precisely. Two provisions do the work. 4A-202(a) makes an order the authorized order of the person named as sender if that person authorized it. 4A-202(b) goes further: where the bank and its customer have agreed to verify orders by a security procedure, a payment order is effective as the customer's order "whether or not authorized" if the procedure is a commercially reasonable method of guarding against unauthorized orders and the bank proves it accepted the order in good faith and in compliance with that procedure. 4A-202(c) then makes commercial reasonableness a question of law, judged on the customer's circumstances and the procedures in general use, and deems a procedure reasonable where the customer refused one the bank offered and agreed in writing to be bound instead. The practical upshot is that the argument "I did not really authorize this because I was deceived" is not the argument Article 4A is set up to hear.
The money-back guarantee, which is the part almost nobody knows. 4A-402(c) provides that a sender's obligation to pay its payment order "is excused if the funds transfer is not completed by acceptance by the beneficiary's bank." 4A-402(d) then obliges a bank that received payment to refund it to the extent the sender was not obliged to pay, "and interest is payable on the refundable amount from the date of payment." 4A-402(f) makes both rights immune from contract: they "may not be varied by agreement." So a transfer that fails somewhere in the chain is not a loss to be negotiated. It is a refund the bank owes, with interest, on terms the account agreement cannot rewrite. That is a different question from a transfer that reached exactly the account you named.
Cancellation has a hard edge, and the edge is acceptance. Under 4A-211(b) a cancellation is effective if notice reaches the receiving bank in time and in a manner affording it a reasonable opportunity to act before it accepts the order. Under 4A-211(c), once an order has been accepted, cancellation "is not effective unless the receiving bank agrees or a funds-transfer system rule allows cancellation or amendment without agreement of the bank." Before acceptance you have a right; after acceptance you have a request. This is why the useful thing to do in the first minutes after a mistaken wire is to call and ask, in those words, for a recall.
Regulation E, stated the way the regulation states it. 12 CFR 1005.3(c)(3) excludes from the definition of an electronic fund transfer "any transfer of funds through Fedwire or through a similar wire transfer system that is used primarily for transfers between financial institutions or between businesses." The exclusion is written in terms of the system, not the instrument, and it is an exclusion from Regulation E's subpart A. It does not put wires outside Regulation E altogether. A wire a consumer sends to a recipient abroad is a remittance transfer under subpart B, which applies regardless of whether the transaction is also an electronic fund transfer, and that carries its own set of rights including a short cancellation window. A domestic consumer wire is the one genuinely outside the subpart A consumer procedures.
The recurring practical hazard is the account number, and Article 4A says so in terms. Under 4A-207(b)(1), where a payment order identifies the beneficiary by both name and account number and the two identify different people, the beneficiary's bank may rely on the number if it does not know of the discrepancy, and it "need not determine whether the name and number refer to the same person." 4A-207(c)(2) leaves a consumer sender one opening: an originator who is not a bank, and who proves the person identified by the number was not entitled to receive the payment, is not obliged to pay the order unless the originator's bank proves the originator had notice, before acceptance, that payment might be made on the number alone. Banks give that notice in the account agreement as a matter of routine, which is why the practical answer is usually that a wrong account number is the sender's problem. Confirming payment instructions by a phone number you already had, rather than one supplied in the same message as the instructions, is the step that prevents the common version of this.