Both test the engines sealing capability.
One while in motion the other at rest.
The leak down will show the total amount of leakage past the rings, valves(4 stroke) and gaskets. As you inject air and note where it escapes, this will tell you where a problem lies. (4cycle) carb= intake valve, exaust pipe= exaust valve, crank case filler= piston ring blowby.
You can check for wear in a cylinder by compairing leakage at TDC to BDC or just before the rings cross the exaust port opening.
On a compression test the first pulse will give you an idea of wear in the cylinder.
A compression test with all cylinders even and high is considerded good.
Leak down. Less than 10% to 15% I would guess is OK, not perfect but OK. Depending on ring end gap or/and top pinned rings I remember 15% to 20%
What you want is to check, record and the compare over time. As wear takes place leakage increases. Also as carbon builds up compression increases.