I am confused between the difference of these two forms of conditional logic

not A -> B

not B -> A

versus

A -> not B

B -> not A

Do both forms above really mean either or, but not both?

In one of the games explanations, I remember coming across a point that starting with a negative term as the sufficient condition, meaning where the absence of a sufficient condition guarantees a necessary condition is somehow different than starting with a positive term for the sufficient where the presence of a sufficient condition guarantees the necessary condition. BUT I am having trouble seeing if there is a difference in the meaning of the above two forms and hat kinds of inference I can make from them.

Can someone please clarify this? I am really confused.

Thanks,

Pamela