Bash is an sh-compatible command language interpreter that executes commands read from the standard input or from a file

Shell is a UNIX  term for the interactive user interface with an operating system. The shell is the layer of programming that understands and executes the commands a user enters. In some systems, the shell is called a command interpreter. A shell usually implies an interface with a command syntax (think of the DOS operating system and its "C:>" prompts and user commands such as "dir" and "edit").
As the outer layer of an operating system, a shell can be contrasted with the kernel, the operating system's inmost layer or core of services.