Debian-Installer
Debian-Installer is an installation program designed for the Debian Linux distribution. It originally appeared in Debian release 3.1 (Sarge), released on June 6, 2005, although the first release of a Linux distribution it was used with was Skolelinux Venus (1.0).
It is also one of two official installers available for Ubuntu; the other being called Ubiquity (itself based on parts of debian-installer) which was introduced in Ubuntu 6.06 (Dapper Drake).
It makes use of cdebconf (a reimplementation of debconf in C) to perform configuration at install time.
Originally, it only supported text-mode and ncurses. A graphical front-end (using GTK+-DirectFB) was first introduced in Debian 4.0 (Etch). Since Debian 6.0 (Squeeze), it uses Xorg instead of DirectFB.
debootstrap
debootstrap is a software which allows to install a Debian base system into a subdirectory of another, already installed operating system. It needs access to a Debian repository and doesn't require an installation CD. It can also be installed and run from another operating system or to create a "cross-debootstrapping", a rootfs for a machine of a different architecture, for instance, OpenRISC. There is also a largely equivalent version written in C – cdebootstrap, which is used in debian-installer.