Hello RyanWoods60,
If they are showing up as a green messages, then these would be sent as a text message.
Learn more here: What is the difference between iMessage and SMS/MMS? - Apple Support
If she normally uses iMessage, but the device is off, then it wouldn't be able to be delivered. The message will then turn from an iMessage to a text message, with a message informing you of how it was delivered. Following messages would be sent as text, until iMessage is available again. It wouldn't inform you of this, since the bubbles continue to show up as green in color.
If she doesn't turn back on the phone before you send another message, the following morning. Nothing has changed and it would be delivered as a text message, until she turns back on the device. It wouldn't need to inform you that it was a text, since it wasn't originally sent as an iMessage.
Hoping this helps out.
Take care.