Both sides are Apple phones. I sent a text message to the other party, and the mobile phone shows that it has been delivered, so did the other party receive it?

Yes, the monitor has been delivered, indicating that the other party has received it, but it is unknown whether it has been read. If you want to know whether the other party has seen it, you can press the following settings:

In Settings-Message-imessage-Send Read Receipt, after this switch is turned on, the other party will read your message and you will be notified. When you send an imessage, it shows that it has been sent, which just means that the message has been sent, and the other party may not have read it yet.