Regardless of the type of message you are sending, the handling looks like this:
sender's phone >> sender's server >> receiver's server >> receiver's phone
Once the message leaves your phone, you have no control over anything related to that message.
Most apps support "delivery receipts", which can tell the sender that the message arrived on the receiver's phone.
Some apps support "read receipts" (most do not) letting you know that the receiver actually read the message. Most apps that support these read receipts also the user to turn them off so that the sender gets no feedback.