Will there be such a situation, you received the receipt of the text message, but the other party did not receive the text message?

Certainly not, because only when the other party's mobile phone receives the short message will the mobile phone send the received signal to the network operator, and then the network operator will send you the status report. If the other party doesn't receive the short message, it won't send the received signal to the network operator, and you won't receive the status report, so there is no situation that the other party doesn't receive the short message and you receive the status report.