Yes, normally one sees, or doesn't see, a difference between two things.
One often makes a distinction between things, i.e. one takes care to distinguish between them, not confusing them or treating them as if they were the same.
(The association with "specialness" isn't directly relevant here.)
I agree with the last part of #1.
In the suggested version I would just put in a comma before "or", and not necessarily repeat "sentence".