Great info and references Joseph. But it looks to me like neither one does quite what he asked about. That could be my misread of the reference material (see below)
Actually, the install of DSL designed just for Flash drives currently allows you to store your settings (home dir) in a file on the same drive
( http://www.damnsmalllinux.org/wiki/index.php/FAQ#How_do_I_save_my_settings.3F)
Puppy Linux also is designed to work correctly entirely off the flash drive, including /home (/root actually, since it defaults to running as root). It uses UnionFS to unify the flash partition(s) (Puppy stores them in files for speed of boot, since it copies the whole system into RAM) along with a user partition stored in a special file on the same drive (all changes end up here). It's done that way to enable efficient copy-on-change for the whole system, still permit auto-detect to work, and work with a unified image for both flash and CD (the CD has the same support for a writable file for the user's changes).
(http://puppylinux.org/wikka/FlashDetail)
In both cases, you get a functioning system that does exactly what was originally asked, that is that it runs well from USB flash (both systems have no swap partition, but will use one if available otherwise), and retains settings between sessions, like any normal install.
It's not terribly obvious on the sites for both systems, but it does work this way. The way both systems store the data (in a file) is done for three reasons:
1) Both systems are designed to be EXTREMELY frugal about writes to flash, and the settings file is only updated on shutdown (it's all in memory the rest of the time).
2) Using a file like this works better with UnionFS and with loading the whole system into RAM (which really speeds up the system).
3) The file can often be stored on someone else's filesystem (Windows NTFS/FAT16/FAT32, Linux Ext3, etc...), enabling you to share a friend/roommate's computer without disturbing their OS, regardless of their choice of OS.
==Joseph++