Is CentOS exactly the same as RHEL?

CentOS is very close to being RHEL without the branding and support. In particular, the library versions are the same, so binaries that work on one will work on the other. The administration tools are the same and configured in similar ways. However, there are a few differences, as the two distributions sometimes apply different minor patches. For example, in this question, it was apparent that RHEL 5 and CentOS 5 apply different rules to identify files under /etc/cron.d.

In other words, at the level of your course, you can treat CentOS and RHEL as interchangeable. But if you needed to look up the precise behavior of a program in a corner of the man page, you may encounter differences.

This may answer your question. Here's an excerpt from the page.

CentOS is a free operating system distribution based upon the Linux kernel. It is derived entirely from the Red Hat Enterprise Linux (RHEL) distribution. CentOS exists to provide a free enterprise class computing platform and strives to maintain 100% binary compatibility with its upstream source, Red Hat.[2] CentOS stands for Community ENTerprise Operating System. CentOS is the most popular Linux distribution for web servers with almost 30% of all Linux web servers using it

No. Although it's close. There are some key differences.

• CentOS lacks certified cryptographic protection required on government networks.
• CVEs (Common Vulnerabilities and Exposures) are not tested on CentOS, and it is expensive to test them properly.