The fenders have a bigger radius than the pickup and the lower portion of the grill shell is narrower to accommodate the bigger fenders.
While the basic cabs are the same, the mounting wood between the cab and the frame is different and the holes in the cab and frame are different, especially at the rear corners. I believe the grills are the same as two different parts numbers or prefixes are not given to distinguish one grill from another.
Here is a good thread on 35 to 37 pickup differences from the Hamb, which includes the differences between the big truck and pickup, including the grill she'll difference.
http://www.jalopyjournal.com/forum/threads/1935-1936-ford-pickup-tech-for-the-masses.236409/