The answer is
The difference of 73.
Long story short (look below if you want to see the deductions):
Using deductions without taking maximization into consideration you can only get this far:
So whatever is the final solution it has to resemble this.
To maximize:
We see that we can easily make the bottom right square 1 without taking anything away from the top left and from here we need to make top left yellow and everything else too to maximize the difference.
Sadly
From here on out you can have two ways to complete the grid.
However
if we want the higest difference plus a unique solution we can make the bottom right 2 making 72 the difference!
The solution path:
Starting off with the ones being obviously shaded it forces the 2 to be shaded for if it was yellow then it would lead to a >2 region. 3 has to be yellow so as to not imprison the 2. Then the square to the right of the 2 has to be shaded otherwise the 3 region would be too large:
Next
The 4 cannot be yellow as it leads to the 5 being shaded but this leads to a no hoper for a 5 squared rectangle as the only two ways to make one makes the 4 region too big and so 4 needs to be shaded…
This forces:
Then
For the 6, a similar issue arises as for the 4 if it was yellow- it is a no hoper for the 7 rectangle as the only two ways of making one makes the 6 region too big:
Then this forces:
Then
8 being yellow leads for no possibility for a 7 and 8 segment to co-exist:
And so this forces:
Finishing off
The 7 segment then needs to me made like so so that it does not violate the rule that the shaded regions have to form a rectangle. The bottom right question-marked region has to be grey otherwise there would not be enough for a 9 sized region and the other shaded area is forced on R1C7 to prevent the size of the region being too big:
