Seems like it's upto the businesses to treat an issued card as debit or credit. I can even see use cases for overdraft.
Below is a snippet from their doc[1]
> Any use of an issued card that results in funds entering or leaving your Stripe account
Here's what I've understood so far.
1. Businesses create, maintain and own customer accounts. It's upto the businesses to figure out how to get money from the customers. Could be prefunded (i.e., debit card) or postpaid (i.e., credit card).
2. Said business then creates cards and associates them with the above customer accounts and issues them that card.
3. Customers are now enabled to use those card wherever credit/debit cards are accepted.
4. Businesses need to maintain balance with Stripe. Stripe deducts from this account upon successful authorisation.
5. Now as I've mentioned in #1 it's upto the business to figure out a way to charge the customer.
Money movement is happening in two steps.
1. Business account -> Merchant (via stripe).
2. Consumer -> Business (Stripe isn't involved here).
Whether #2 happens before or after determines if the card is a debit card or credit card respectively.
So, what Stripe has done essentially is connect accounts holding money with rest of the world. I.e., anyone can now become a bank, in a sense.
In my previous job my team worked with a similar third party provider to launch a virtual card product[2]. But what Stripe has done is game changing.
[1] https://stripe.com/docs/issuing/transactions [2] https://www.freecharge.in/mobile/freecharge-go
Edit: Minor correction.