A sale made directly on an Odoo-built storefront updates inventory and triggers an invoice the same way any other Odoo sale does, since it's all one system. A sale made on Amazon or eBay happens entirely outside Odoo, which means someone has to get that order into Odoo to update stock and books, and get current inventory levels back out to the marketplace so it doesn't oversell.
The same gap shows up for a business migrating onto Odoo's storefront from an existing separate site. Running both in parallel during the transition, keeping products, prices, and orders consistent across the old site and the new one, isn't something either platform handles without a bridge built specifically for that migration window.