The split that decides everything is where the money rests. In a rail-based service, the app is an addressing and routing layer over the banking system: your bank is debited, the recipient's bank is credited, and nothing of yours is ever held by the provider. In a stored-balance service, received money accumulates in a balance held by the provider until you move it out, and that balance is an obligation of a technology company rather than a deposit at a bank. Many services now do both, which is why the question is about a particular payment rather than about a brand.
A stored balance is not a bank deposit, and the difference is not cosmetic. Providers typically place pooled customer funds at one or more partner banks, and federal deposit insurance can reach an individual customer's share of that pool through rules that treat the provider as holding the money on the customer's behalf. That works when the recordkeeping is accurate enough to establish who owns which share. It is not a promise the user can verify, the determination is made only when a bank actually fails, and it protects against the bank failing rather than against the provider failing. The fintech page covers the pass-through mechanics; the shorter version worth carrying is that a balance left in an app is money in a place whose protection depends on somebody else's bookkeeping.
Who pressed the button decides who bears a loss. Regulation E's protections for unauthorized transfers are strong, and they apply to these apps in the ordinary way: a transfer someone else initiates from your account, including after tricking you into revealing a login or a texted code, is unauthorized, and your liability is capped by how quickly you report. A payment you initiated yourself is not unauthorized under the regulation, whatever you were told to induce it, and the error-resolution rules do not contain a limb for goods that never arrive. That is the whole reason the standing advice about these apps is to treat them like cash between people you know.
Buyer protection, where it exists, is contractual. Several providers offer protection on payments flagged as being for goods and services, usually in exchange for a percentage fee charged to one side of the transaction. That protection is a term of the provider's user agreement. It is not a statutory right, its scope is defined by the agreement rather than by a regulation, it can be amended, and it does not attach at all to a payment sent as a personal transfer. Reclassifying a payment after the fact is generally not possible, which makes the choice at the moment of sending the operative one.
Two smaller mechanics that cause real problems. First, payments are addressed to tokens, and a token can be mistyped or can belong to someone who is not who the display name suggests, because the name shown to a sender is supplied by the recipient's enrollment rather than verified against a legal identity. Second, receiving business income through one of these apps is a reporting event, and the thresholds and forms involved have changed more than once, so a person selling regularly through a payment app has a tax question as well as a payments question.