Some Sudoku grids have the pattern:
ABC ABC
CAB - or - BCA
BCA CAB
where each 3x3 grid in the positions labelled A is the same except
possible for permutation of rows and columns, and similarly for the
grids in the positions labelled B or the positions labelled C.
Here is one such example:
123 456 789
456 789 123
789 123 456
456 789 123
789 123 456
123 456 789
789 123 456
123 456 789
456 789 123
But some Sudoku grids are not like that.
For example, the grid below is not of this form since 534 is the first
row of the upper left 3x3 grid, but the numbers 534 do not appear (in
any order) as a row in any of the four 3x3 grids in the bottom right.
534 678 912
672 195 348
198 342 567
859 761 423
426 853 791
713 924 856
961 537 284
287 419 635
345 286 179
If the Sudoku grid is of this form and I permute numbers, or permute
the groups of 3 rows, or groups of 3 columns, or permute the rows or
columns within any of those groups, then it is easy to see that the
grid will still be of that form.
If it is not of that form then these permutations will not put it in
that form. Thus, the two grids about cannot be transformed into each
other.
(This is true even if you allow reflection as another transformation
and if you freely permute the rows or columns within each of the 3
groups without regard to how the other rows and columns are being
permuted.
In fact, if you allow all of these transformations then there are
5,472,730,538 distinct grids according to J.-P. Delahaye, "Le tsunami
du Sudoku" in 'Pour La Science' (French Edition of "Scientific
American"), December 2005 pp. 144-9, Paris.