The discrepancy in the number of purchases may be because the customer has opted to checkout on Facebook (using Facebook’s checkout) as opposed to checking out on your website. Shopify does not have access to the order information on the Facebook checkout, so it will not be recorded in your store.
To check out on your website, they must select “View on website” to be redirected to your Shopify store, where they can complete their purchase. Only then would Shopify be able to record the order made, as it would have been made through the Shopify platform.
You can learn more about this via this thread.
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