How can I tell if a text message has really been sent?

In your text message history, you can view a given message's status as assigned by the recipient's text message server once the message has been actually sent or not sent.

This is what these explanations mean:

Pending: the end operator has not succeeded in transmitting it to the recipient, for example when the mobile isn't switched on;

Sent: the message has been received on the mobile

Not sent: the number the message was sent to isn't valid (for our server: wrong number, or wrong provider), or the waiting period for sending it has expired (24h, which is the maximum authorised by our server).