Linux is a trademark of Linus Torvalds Who is a creator of Linux Kernel, So any Operating System using linux kernel called as a Linux. Linux Kernel is a part of Linux Operating System, It is not a Whole Operating System.
There is a Big History About it, in short Other part of operating system is taken from GNU so any operating system with Linux kernel and GNU packages called GNU/Linux.
CentOS is a project to provide Enterprise-class Linux Distribution, RHEL is using GNU Components for Complete Operating System so As per GNU's GPL license they must publishing their Source Code
CentOS grabs source code and recompiling it and clean-out trademarks and packaging it.
So its a very clear thing that CEntOS is a Free and Open Source Clone/Fork Of Red-Hat Enterprise Linux Operating System.
CentOS is benig very popular, It is free and open source GNU/Linux Operating system.