"dpkg" is short for "Debian Packager". dpkg is a low-level package manager for Debian-based systems. It can install, remove, provide information about and build *.deb packages but it can’t automatically download and install their corresponding dependencies.
apt (Advanced Packaging Tool) is a Shell front-end package in Debian and Ubuntu Manager.
apt is a high-level package manager for Debian and derivatives, and provides a simple way to retrieve and install packages, including dependency resolution, from multiple sources using the command line. Unlike dpkg, apt-get does not work directly with *.deb files, but with the package proper name.
aptitude is another high-level package manager for Debian-based systems, and can be used to perform management tasks (installing, upgrading, and removing packages, also handling dependency resolution automatically) in a fast and easy way. It provides the same functionality as apt-get and additional ones, such as offering access to several versions of a package.
rpm(redhat package manager) is the package management system used by Linux Standard Base (LSB)-compliant distributions for low-level handling of packages. Just like dpkg, it can query, install, verify, upgrade, and remove packages, and is more frequently used by Fedora-based distributions, such as RHEL and CentOS.
yum (Yellow dog Updater, Modified) is a web service in Fedora, RedHat and SUSE Shell Front End Package Manager.
yum adds the functionality of automatic updates and package management with dependency management to RPM-based systems. As a high-level tool, like apt-get or aptitude, yum works with repositories.