1. A shell is a basic system program that interprets keyboard and mousecommands. The ash shell is a clone of Berkeley's Bourne shell(sh). Ash supports all of the standard sh shell commands, but is considerably smaller than sh. The ash shell lacks some Bourne shell features (for example, command-line histories), but uses considerably less memory. You should install ash if you need a lightweight shell with many of the same capabilities as the sh shell. From Redhat 8.0 RPM

2. NetBSD /bin/sh "ash" is a POSIX compliant shell that is much smaller than "bash". We take advantage of that by making it the shell on the installation root floppy, where space is at a premium. It can be usefully installed as /bin/sh (because it executes scripts somewhat faster than "bash"), or as the default shell either of root or of a second user with a userid of 0 (because it depends on fewer libraries, and is therefore less likely to be affected by an upgrade problem or a disk failure). It is also useful for checking that a script uses only POSIX syntax. "bash" is a better shell for most users, since it has some nice features absent from "ash", and is a required part of the system. From Debian 3.0r0 APT