When viewing SMS receipts, you will notice that some texts will report as being "Accepted by Carrier" and others as "Delivered to Handset".
Accepted by Carrier: The text has been transmitted to and accepted by the recipient's mobile carrier. It will be processed and, if possible, delivered. This is typically the final "success" status returned for SMS, as not all carriers or carrier equipment will support any further tracking and receipts.
Delivered to Handset: This status indicates that the text message was not only accepted by the mobile carrier, but the carrier has confirmed that the message reached the end user's mobile device (their "handset"). This status means the message was on the user's phone. This is the most detailed delivery receipt possible for standard, cross-carrier, cross-platform text messaging.
Please note that SMS receipts are not guaranteed to be returned by mobile carriers in "real time". Some carriers send them right away, but many send receipts in batches over time. Carriers prioritize delivery over reporting, so reports can lag significantly behind the actual delivery time for a text.
It's not uncommon a message to change from "Accepted by Carrier" to "Delivered to Handset". This often occurs several minutes or even hours after the text has been delivered to the user's device. The text may arrive in seconds, even if the "delivered" receipt comes back much later.