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The difference between wake up and get up is very small. But I thought it would be beneficial to know the exact difference. Wake up is when you wake up from sleep. Get up is when you get out of bed. Usually, when people wake up, they get up. However, sometimes people just stay in bed. In that situation, they couldn't use these two words interchangeably. Here is an example dialog showing the difference.
Person A: 'When did you get up this morning?'
Person B: 'I got up at 11.'
Person A: 'You slept at 11 last night. So you slept for 12 hours?'
Person B: 'No. I actually woke up at 9, but I just stayed in bed.'
When you talk to people, go ahead and use either of these two words. Just keep in mind that there is a small difference.
On a side note. When you ask someone when they woke up, you don't use the past tense of 'woke' although it is referring to the past. 'What time did you woke up this morning' is incorrect. The correct way to ask this question is, 'What time did you wake up this morning?'
Likewise, you wouldn't say, 'What time did you got up?' The correct way to say this is, 'What time did you get up?'