See AshSh for more information
Index of the Ash command line

Puppy is moving to and supporting the full Bash

ash or bash in Puppy (others exist, such as Korn and C shells)
See also: ShellScripts

sh is the default shell, which in 1.0.5 and 1.0.6 is ash or bash
(In 1.0.6, SHELL seems to point to bash, but the command line seems to nevertheless default to ash.)

ash is the simplified BusyBox version of bash (BusyBox v0.60.5 in 1.0.6)

Bash, an acronym for "Bourne−Again Shell" and a pun on Stephen Bourne's now classic
Bourne Shell. Bash has become a de facto standard for shell scripting on all flavors of UNIX.
The bash is GNU bash 3.00.0(1) in 1.0.6.

http://www.gnu.org/software/bash/bash.html∞
http://www.tldp.org/LDP/abs/abs-guide.pdf∞
Advanced Bash−Scripting Guide. An in−depth exploration of the art of shell scripting.

LinuxWiki

external links:
http://www.wlug.org.nz/Shell∞
http://www.wlug.org.nz/ash(1∞)
http://linux.about.com/library/cmd/blcmdl1_ash.htm∞
http://www.debian.org/doc/manuals/reference/ch-program.en.html∞
http://www.phenix.bnl.gov/WWW/offline/tutorials/debuggingTips.html∞