Twilio will only charge your Twilio project for sending messages through our API. We will not charge the recipient of your message for receiving a Twilio message. However, it's possible that the recipient can be charged by their phone provider.
Different mobile plans have different agreements for messaging. Some mobile plans may charge the recipient to receive messages, while some don't. This depends on the mobile plan your recipients are using.
Twilio does not offer premium SMS messaging where the cost of receiving a message can be passed on to the sender.