Integrating sales transactions into accounting software

How do startups get their sales transactions into their accounting software (Quickbooks, cloud based software, or whatever is used)?

I assume with your typical web app credit card processing is done with Stripe, Braintree, etc., how should each individual sales transaction make it into the accounting software.

Do they have each sale end up being recorded along in a PostgreSQL database? But then this needs to be exported to the accounting software that is used. It would make a lot of sense for the entire pipeline to be automated obviously.

Really what I'm asking is what is the common practice software architecture to handle a sales end to end?