MIRO is online invoice posting, which means you can simulate and check the value and post online (in other words Foreground )
MIRA is posting happens in background, you will enter the details and the posting take place in back ground.
You can run both transaction simultaneously for different PO's and not for the same.
Please let me know if have any clarification
MIRO is for Invoice verification for a single PO.
MIRA is a transaction for the invoice verification in background. It is used dif you have a large number of items in the invoice and instead of entering everything manually we use MIRA.
There is a programme need to be run to start the invoice verification in background. The R/3 System checks invoices in the background using settlement program RMBABG00 and posts them.