Both can be used to describe a physical position, higher than another, referenced position or object.
The bird hovered above the river.
The bird hovered over the river.
ABOVE describes a static, higher position.
OVER can mean ABOVE but can also indicate movement (to traverse), as in: "She walked over the bridge."
OVER can also mean "ON THE OTHER SIDE OF" - "The restaurant is over the river, on the other side."
OVER can also mean "BEYOND" - "Somewhere Over the Rainbow." - "That was over the top!"
Sometimes we say them together (for emphasis): "Her efforts went over and above what was required."