Medium is the everyday Kakuro tier — it is also the difficulty of the daily puzzle. These boards verified as needing more than surface reading: somewhere in the solve you must bound a cell by what its run's other cells can still contribute, or eliminate digit combinations a clue can no longer use, before the next placement appears.
The rhythm is: place the forced digits, then when the board quiets down, pick a tight clue and interrogate it — which of its combinations survive the digits already on the board? The survivors usually agree on something.
If a medium board stalls, the strategy notes cover bounding and elimination with worked examples. Comfortable here? The hard bucket adds pair logic.