MT (Mobile Terminated) billing is where a handset is charged each time a premium message is sent to it. The number has to subscribe to the service first in order to accept chargeable messages. If a handset hasn't subscribed or has sent in 'stop' or 'stop all' to the shortcode, any premium message will be marked as 'Failed Authorisation' and will be blocked before it reaches to network.
MO (Mobile Originated) billing is where the handset is charged when a message is sent from the phone into a premium service.
