Is spend data exported as purchase invoices or other payments?

Both, depending on the type of expense, these can either be exported as purchase invoices or other payments.  

A transaction will be exported as a 'purchase invoice' when it has an invoice attached to it and might have been paid in a different currency to your account currency.  

A transaction will be exported as an ‘other payment’ when it doesn’t have an attachment or, has a receipt or mail attached to the transaction and is the same as the base currency.