[tsubaki]

Normally when they repitch a prop, they heat and bend the blades causing the need to rehub. Actually, if I'm not mistaken they have to remove the hub to fit their presses.
Lets say you repitch from a 15 to a 17, you will lose diameter. If you repitch from say a 17 to a 15 you may need grinding to fit beneath the cavitation plate or miss the steering torque.
When buying new, there are numerous changes that can be made toward performance with subtle changes of the prop, this is where the pro's come into place.
Depending on the circumstance, keeping a certain pitch but changing the diameter or even the blade design cup or lack there of can make a huge difference in performance. The same can be said for keeping a certain diameter and changing the pitch, having a cupped or regular blade.
The diameter basically dictates how much water the prop grabs BUT there is almost always a relationship with the pitch.
What I do is find a normal manufacturer of a prop (Michigan Wheel preferred) and work within the perimeters of their props. Easier to replace with the same if damaged.
Lets say I've got an engine not turning up enough rpms and have verified the engine is running correctly and at the correct height. I'd decrease the pitch a couple of numbers, test and go from there. You will see the average manufacturer does not carry the same diameter while also changing pitches.
Now, problematically, different prop materials will change your prop designations. Stainless, aluminum or composite materials perform differently even if you have the same exact pitch, diameter and blade design between the three.
Sorry this is not a good definition but about the best I can muster.