I don't know that the banks "tell" vendors "This purchase was made with a pre-paid credit/bank card" - I've not seen a flag that shows that before.
As a former Redbox employee told me: this is a premium service from card issuers.
You can find lists of the BIN numbers for prepaid cards. Also, in the US, most of them fail AVS checks with a 'U' code.
Stripe give you a `funding` property on a card source [0], which at least in the UK distinguishes between debit, credit and prepaid cards somewhat reliably.