When your alarm rings in the morning you 'wake up' as you are no longer sleeping. 'Get up' means that you get out of bed. 'I wake up at 7am, but i don't get up until 7:30.

Wake up is when you open your eyes and leave the dreams behind. To get up you need to move your body upwards from sleeping or just resting.

Hey! Wake up means you wake up from sleeping. You can only use this when you wake up from sleeping before. Get up can mean that you stood up from sitting down or sat up from lying down. Get up is more of an overall, general term for the action of coming up.