Bash is the gnu shell which is a superset not posix which is basic no frills mixture of minimal ksh and bourne syntax.
BSD has the almquist shell as it's /bin/sh and tcsh as it's /bin/csh. Various commercial vendors licensed the korn shell from bell labs. The korn shell is public domain and open for 13 years now. The default sh on most UNIX boxes are either ash or a hard link to ksh which emulates the POSIX definition of sh. zsh and bash also provide the option to hard or soft link so depending on your distro you may have /bin/sh linked to bash.
Debian at one point repackaged the BSD almquist shell as their system sh calling it dash mainly for speed and stability. I believe they removed it as their programmers apparently couldn't program system level scripts without their non portable bashisms or maybe just one of the NIH moments where everything must live under a single mono-cultural license and identity.
(about Debian use of dash)
> I believe they removed it ...
No, /bin/sh still points to dash in the latest and just released Debian stable (Wheezy). It seems to me that this transition was already completed in Sequeeze but I haven't checked.
