  In this paper, we focus on the difference analogue of Stothers-Mason theorem
for entire functions of order less than 1, which can be seen as difference
$abc$ theorem for entire functions with slow growth. We also obtain the
difference analogue of truncated version of Nevanlinna second main theorem
which reveals that meromorphic functions which are of hyper order less than 1
except periodic functions with period one cannot have too many points with long
height in the complex plane. Both theorems depend on new definitions of height
of shifting poles and shifting zeros of a given meromorphic function in a
domain.
