Approximate modified duration vs Effective Duration

May I know the difference between Approximate modified duration vs Effective Duration, their formula look exactly the same.

Beside, why effective duration is suitable for embedded option bond? Because it use the Exact value (Up/Donw) for calculating the duration?


Beside, the same problem on Effective convexity and approximate effective convexity, it look almost the same.

Modified duration assumes that cash flows will not change when yield changes.

Effective duration allows for cash flow changes when yield changes.

The formulae are the same; the up and down prices may be different.