Don't know... but they are different. The headlamp arrangement is different, on the J a bracket passes through a big hole in the wing and the P engine is I think 2" longer so presumably the wing is slightly longer too...
The P type was delayed in entering into production and the P wings were used on the later J types to give them a slightly more modern and practical appearance which helped sell the last of the production J types. Therefore, you have the basic shape there to modify regarding the points Peter raises
Could that then mean that to accommodate Peter's mention of engine length, the J2 used a shorter running board? This relatively small item would have been a cheap solution after all.