Volusion's API covers the core commerce objects, orders, products, customers, in a programmatic, token-authenticated way, similar in spirit to other hosted platforms' APIs even if the public documentation is thinner than what you'd find for a bigger name like Shopify.
On some Volusion plans, store owners have historically had direct access to the underlying database, a level of access most hosted platforms don't offer at all. It's a genuinely distinctive option: instead of working entirely within an API's limits, a developer can query the store's data directly. It's also riskier, since a bad query runs straight against live store data with no API layer softening the blow.
FTP-based exports and scheduled data dumps cover the rest, useful for bulk catalog updates or periodic reporting, but they're inherently batch work: a change made today might not reflect anywhere else until the next scheduled export runs, not the moment it happens.