Depends on what "texted" actually means. iMessage is Apple's instant messaging service that also knows how to talk to the SMS system.
If your contact is also an iMessage user, the message never left the iMessage system, thus "delivered" means whatever it means in iMessage.
If your contact is not an iMessage user (ie, android user), then "delivered" is still needing a formal definition because of the iMessage-SMS interaction.
In the pure SMS world, "delivered" means that the message was received by the recipient's phone from their carrier's server. What the recipient's phone did with the message is unknown to the sender (saved to the inbox, blocked/rejected/discarded, saved to the spam folder, read).