Sudoku Difference

If a row, column or block contains $8$ determined numbers, the final number is also determined. If all but $1$ , $2$ or $3$ numbers in the whole grid are determined, there must be at least one row or column which contains $8$ determined numbers and one of the undetermined ones. But means that one of the undetermined numbers must in fact be known.

This means that the smallest number of squares by which two grids can differ is $\boxed{4}$ . The grid below shows an example. The numbers $1$ and $6$ in the four shaded squares could be exchanged.

The minimum no. of squares that can differ implies we aim to keep most of the two sudokus identical.

It can't be just 1 square because no square can possibly have two solutions.

It can't be 2 squares because that means you exchanged two numbers with each other in the 2nd sudoku, & we now have an unstable sudoku with 1 row, column or big square that have a number twice and is missing the other number

4 squares with a pair of numbers would be a stable solution. You need a pair of number to exchange them only with each other in order to keep rest of the solution same but that would create instability as we saw above. So you need to exchange them twice, so as no one number, of the two, repeats itself in it's row/column & is not missing from another row/column.