The exploitation phase involves taking advantage of the previously discovered vulnerabilities. This stage is the actual attack phase. In this phase, a penetration tester fires up exploits at the target vulnerabilities of a system to gain access. This phase is covered heavily throughout the book.
The post-exploitation phase is the latter phase of exploitation. This stage covers various tasks that we can perform on an exploited system, such as elevating privileges, uploading/downloading files, pivoting, and so on.