Your Facebook Shop customers might have a different experience based on a few things.
Some stores will use Facebook's integrated checkout. Other stores might automatically direct customers to your Shopify checkout when they choose to pay for their products. If your store is eligible to use both checkouts, you can choose which one to use in your Facebook sales channel settings.
If you use Facebook checkout, customers can purchase from your Facebook Shop directly on Facebook without being redirected to your online store. They automatically receive confirmation emails about their orders from Facebook, and their orders appear on both the Orders page of your Shopify admin and the Purchase History of their Facebook account.
Customers can't use Shopify discount codes for purchases on Facebook.
If you use Shopify checkout, customers who purchase items from your Facebook Shop are redirected to your Shopify checkout to complete their transactions. They automatically receive confirmation emails about their orders from your store, and their orders appear on the Orders page of your Shopify admin.
Your customers can contact you directly using the Contact Seller button in their receipt and in their Purchase History in Facebook. This button will forward customer inquiries to the customer support email you have on file with Shopify. According to Facebook's Sales Policy, you have ten business days to respond to your customers' inquiries before they have the option to escalate their issues to Facebook's customer service.
Facebook requires that you handle customer information gathered through your Facebook sales channel according to their Sales Policy, Self-Serve Ads Terms, and Statement of Rights and Responsibilities.