Sitting Down and Sitting Up

I was thinking, When you are sitting up you are in a sitting position and when you are sitting up you are in a sitting position also. So what is the difference? Well, it came quite clear to me that sitting up is when you were originally in a laying down position. Sitting down is when you were originally in a standing up position. Well I didn't stop there.
It's fine and dandy to command someone to sit down or sit up but what about when  you inform someone you are sitting down. For example "I am sitting down" and "I am sitting up". If sitting is the verb and up and down are the adjectives than how do two opposite adjectives describe the same thing?! This is making me think they are just slang.
Also, when there is a point (Sitting) with 2 possible paths to take to get to that one point (Sitting Down, Sitting Up) than does that bypass the lost info if not knowing which math was taken? Although this last point is a stretch...
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