MIRO used to post the incoming invoices with the reference to PO, BOL. It has also the provision to make the invoices based on the delivery cost and good issue cost.
FB60 used to post the invoices which are not related to PO. In other words, if you don't have a po and still you need to pay something to vendor, you should use the FB60. FB60 posts a noramal Journal entry.
MIRO: When the invoice is to be posted from MM side. In this we raise a Purchase Order (PO), Goods are received (MIGO) then we do Invoice Receipt (MIRO). Automatically while posting MIRO the FI document gets generated. For this the settings are to be made in FI-MM integration.
FB60: This is a pure FI transaction for vendor invoice posting. where the client do not want to maintain Material Master or do not want to activate MM. then the invoice could be raised from FI side. In this transaction PO and goods receipt details are not required.