Comparing two arrays of unequal length

You can use Tuples to construct all pairs of positions and use Select to pick the pairs that satisfy your condition:

pairs = Tuples[{ Range[Length[array1]], Range[Length[array2]]}];
Select[pairs, array1[[#[[1]]]] - 1 == array2[[#[[2]]]] &]

{{6, 2}, {8, 3}}

You can also use Outer as follows:

Join @@ Outer[If[array1[[#]] - 1 == array2[[#2]], {##}, Nothing] &, 
  Range[Length[array1]], Range[Length[array2]]]

{{6, 2}, {8, 3}}

Yet other ways: variations on Roman's method using Position and Outer combination:

Position[1] @ Outer[Subtract, array1, array2] 
Position[True] @ Outer[Equal, array1 - 1, array2] 
Position[{i_, i_}]@Outer[List, array1 - 1, array2]

{{6, 2}, {8, 3}}

This is a general solution for any condition between the elements of array1 and array2:

Position[Outer[List, array1, array2], {i_, j_} /; j == i - 1]

{{6, 2}, {8, 3}}

@kglr's solutions are simpler than this when the condition is a difference as in the given problem.

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