Re: Size vs pitch?
The two examples you gave would be totally different -- not only from a performance standpoint, but from an application standpoint as well.
Pitch refers to the amount of forward movement the prop pushes the boat in one revolution. 15P = 15 inches. 20P = 20 inches. Now realize that those numbers are theoretical in that the prop operates in a liquid, not a solid so there is some slippage. On a given engine, a prop with low pitch provides good hole shot but would have terrible top end because it would allow the engine to over rev -- sort of like having your car in low gear all the time. Props with higher pitch have reduced hole shot but have much better top end. Too much pitch though causes the engine to lug -- like trying to climb a steep hill in high gear. Happiness is a prop that allows the engine to operate at wide open throttle in the rpm band recommended by the engine manufacturer.
When it comes to diameter, your example was extreme in that you could not install a 20-inch diameter prop on an engine that was designed for say a 13- 15 inch prop. Conversely, installing a 12 - 15 inch prop on an engine or out drive that could have a 20 inch prop would be rediculously inefficient. Small outboards are designed to take 8 - 10 inch props, mid range engines take in the range of 10 - 13 and large engines in 14 - 16 range.