A 'moped' is a 49cc bike that is limited to 30mph or thereabouts. Anything up to 125cc is a 'learner motorcycle'.
If you have a full car licence then you can ride a 'moped' without L plates and carry a passenger (if you passed your test since some date, think it's in 2001, you have to do a CBT).
You can ride a 'moped' on a provisional licence, no passengers, must display L plates provided you have completed a CBT.