Tiny Core installs to disk, and allows you to add/update packages once it's been installed.

Something like Knoppix (at least when I used it) runs exclusively off a disk, and can't be updated once it's been burned.

quoted from main site

Core (11MB) is simply the kernel + core.gz - this is the foundation for user created desktops, servers, or appliances. TinyCore is Core + Xvesa.tcz + Xprogs.tcz + aterm.tcz + fltk-1.3.tcz + flwm.tcz + wbar.tcz