The formal announcement " The princess has been delivered of a healthy baby boy" is passive. She didn't do it alone; someone helped the tot to emerge. It's formal because it's meant to sound portentous and momentous.
The semi-formal announcement "She delivered a baby boy this afternoon" is active. It's a simple statement of what happened and tells us all we need to know.
The same goes for the informal announcement "She had a baby boy this afternoon".