I'm not sure if I fully understand the difference between these two.
Can someone explain why I would use one over the other and how they differ?
Answer
You'd use margin, if you wanted to move a (block) element away from other elements in the document flow. That means it'd push the following elements away / further down. Be aware that vertical margins of adjacent block elements collapse.
If you wanted the element to have no effect on the surrounding elements, you'd use positioning (abs., rel.) and the top, bottom, left and right settings.
With relative positioning, the element will still occupy its original space as when positioned statically. That's why nothing happens, if you just switch from static to relative position. From there, you may then shove it across the surrounding elements.
With absolute positioning, you completely remove the element from the (static) document flow, so it will free up the space it occupied. You may then position it freely - but relative to the next best non-statically positioned element wrapped around it. If there is none, it'll be anchored to the whole page.