A 32 bit program doesn't usually differ intentionally
from a 64 bit one, but there are subtle ways in which code can make assumptions about the platform it is on.
There are assumptions about the size of values in structures, about the storage size of arrays of pointers, the ranges of some of the types, unsafe type conversions, alignment of structure members, just to mention a few things that can cause problems. There are ways to make these things portable, but C programmers have become quite used to 32 bits being the standard word size, so we have been slack at times.
My understanding is that the 64 bit version of Wine
is still not in a stable state.