Texts: difference between delivered and read?

What if the recipent reads the text from a banner pop-up while in another app or from the lock screen, and doesn't navigate to the Messages app?

I had a recent text exchange with a person who insists that they did't Read my messages, while I saw the "read" indication. He's trustworthy. Is this possible? Under what conditions?

think of your physical mailbox.

Delivered : The recipient's phone has received the message.

Read : The recipient has read said message.

No, maybe he was disabled "Send Read Receipts" on his Message Settings.

Open the message with his/her eyes closed?

"Read" means that he/she open the message but you never know if he/she actually read the message.

Yes he or she seen the message pop up on the banner or lock screen. Doesn't mean read but it does mean they have seen the message.