Not X - >Not A and X - >A are completely different statements, and they do differ. Here's how:
Not X - >Not A can also be written as A - >X, which is its contrapositive.
A - >X is a logically equivalent statement to Not X - >Not A since it's its contrapositive.
A - >X and X - >A are totally different things. They have each other's sufficient and necessary conditions switched, so they do not mean the same thing. This is why Not X - >Not A and X - >A are different statements and don't mean the same thing.
Does this make sense? Let us know if you have any other questions!
