Let us use an explicit example. Let A be the event that Adam shows up at the party. Let B be the event that Bill shows up at the party. Suppose that Adam and Bill hate eachother and if are together will start a fight. You have two choices, either to make sure to invite only one or the other, or to invite neither at all.
The phrase "not A and not B" (in symbols: $\sim\!\! A * \sim\!\! B$) can be reworded in more common English as "Neither A nor B is true." In our example, this means that Adam is not at the party, and also Bill is not at the party. So, in this case, we choose not to invite Adam and we choose not to invite Bill. We don't want to be friends with them anymore since they are the type to start a fight. Adam Fred and Charlie being at the party but Bill is stuck at home is not okay. We didn't want Adam there at all.
The phrase "not A and B" (in symbols: $\sim\!\!(A*B)$) can be reworded in more common English as "It is not true that A and B are simultaneously true." In our example, this is the case where we allow ourselves to invite exactly one of Adam or Bill to the party. With them separate, they shouldn't cause any trouble. It is okay for us to have Adam Fred and Charlie at the party with Bill stuck at home. Since Adam is without Bill it is okay.
If your confusion stems from which image to pair with which, the $\sim\!\!(A * B)$ is the opposite shading of the $(A * B)$ image.
The $(\sim\!\! A) * (\sim\!\!B)$ is the opposite shading of the $(A+B)$ image.