What is the difference between normalization and re-scaling?
Re-scaling means that you multiply your variable by a factor, i.e. $x \to x/a$. A normalization is a specific kind of re-scaling, where the factor $a$ is such that the values of $x$ become of order one. Its form depends on the context and what you are trying to do. Examples are $a= \langle x \rangle$ or $a= \textrm{max}(x)$. Perhaps the most common one is when you do $x \to (x-\langle x \rangle)/\sigma$, because if $x$ follows a Gaussian distribution, the re-scaled variable follows a normal distribution (average 0 and std 1). Note, this last transformation actually involves a re-scaling, but also a translation.