What is the difference between Git Bash and the GitHub for Windows shell?
Well, for one thing, the default shell that comes with GitHub for Windows is PoshGit, which is a Windows Power Shell environment for Git. On the other hand, Git Bash/msysGit uses the Bash shell (Bourne Again Shell) and MinGW, which is a port of a Linux style environment and command line tools.
PoshGit will let you use Windows and Power Shell commands with Git at the command line, while Git Bash will let you use MinGW/Linux tools with Git at the command line.