what is meant by minimizing and maximizing in GANs?
This basically boils down to the Vanishing Gradient Problem. It is a well known issue that vanishing gradients limit the ability of deep neural nets to learn. And playing the min-max-game for GANs can lead to this issue for G as well:
When you start to train a GAN G will not produce very good results, i.e. D can easily classify these as fake or real with a probability of them being real approaching $0$. Accordingly, the expression $\log(1-D(G(z))$ converges to $0$, too, and results in a vanishing gradient for G, i.e. the generator cannot really learn when it tries to minimize this.
In contrast, $\log D(G(z))$ does not converge to $0$ when $D(G(z))$ is very small (since $\lim \limits_{x \to 0} \log x=-\infty$). Therefore, G does have a gradient to learn from.
Also see the original paper where the authors write:

Early in learning,
when G is poor, D can reject samples with high confidence because they are clearly different from
the training data. In this case, $\log(1 - D(G(z)))$ saturates. Rather than training G to minimize
$\log(1 - D(G(z)))$ we can train G to maximize $\log D(G(z))$. This objective function results in the
same fixed point of the dynamics of G and D but provides much stronger gradients early in learning.

As you can see, this is a purely practical consideration in order ease learning for G and not about theoretical equivalence of expressions.