What's the difference between "get up" and "stand up"?

I think that there is a connotational difference between the terms.

• Get up clearly denotes an action. You are lying or sitting down, now move, get up.
• Stand up can denote the same thing with regard to physical action.

However, stand up also connotes standing firm, in a sense, a lack of motion, a resolve. This is especially so since it is followed by your rights, which completes a common slogan stand up for your rights. We shall not be moved.

Taken together, the phrases suggest Rise up and stand firm for your rights!

Literally, 'stand up' means you are starting from a lying, sitting, kneeling or otherwise "low" position and at the end you are standing.

'Get up' can mean that, but also means 'wake up' or 'get out of bed'. The result doesn't have to be standing; you can "get up" and end up in a sitting position.

Others have commented on the metaphorical uses of the two, where 'get up' is more about becoming active and 'stand up' is more about resisting.