This isn’t uncommon. The Payments API will show all the payments based on your begin and end time when the payment was created on our servers. However the Dashboard may be showing payments that were completed in offline mode based on the order.tender.created_at timestamp.
Unfortunately, we don’t have documentation on how the Square Dashboard reports are calculated with our APIs nor is there a Reporting API to get this data. However they do use the Orders, Payments, Catalog, Inventory and Customers API to build the various reports based on your needs. 