The main aim behind the SEPA initiative is to improve cross-border payments made in Euro so that they became as simple and cheap as if you were making a local transfer. With this in mind, sending Euros from Germany to a Euro bank account in Greece should be exactly the same as sending the money to another German-based bank account.
Before the introduction of SEPA, transferring money or even paying for goods and services in another Euro country with a debit card sometimes took a long time, plus bank charges often meant that the recipient didn’t get the full amount.