What is a command shell:
Command shell is a program that interprets commands,
Allows a user to execute commands by typing them manually at a terminal or automatically in programs called shell scripts.
A shell is NOT an operating system.
It is a way to interface with the operating system and run commands.
What is BASH:
The name itself is an acronym, BASH = Bourne Again SHell
Bash is a shell written as a free replacement to the standard Bourne Shell /bin/sh originally written by Steve Bourne for UNIX systems.
BASH has all of the features of the original Bourne Shell plus additions that make it easier to program.
BASH is Free Software and was adopted as the default shell on most Linux distributions.