I believe they mean length. 20" is a short shaft, and 24" is a long shaft. (no jokes please)
I'm not sure of the model number. Where would it be on the motor?
The model number is on you transom bracket (starboard side i think) and on a coin sized plug on the back of the block.
you can also measure you transom. top of cavitation plate to top of transom should get you the required measurement. 20" for long shaft, 25" for extra long shaft.