You are elliding two separate things; packages (package formats) and package managers.
For package formats, the popular ones are .deb and .rpm, although some distros use others (you don't actually need a package format - it simplifies the installation and removal of packages - .tar.gz files, which are really just compressed file trees work, but it is the 'do it yourself', or 'write-a-script-for-it yourself' option).
The 'packaged package' is going to have to contain the application itself, information about dependancies, information how to set up the config file and other post-install housekeeping. It should also contain information about what to do on a de-install. But they do, so its not something to get worried about.
Then there are package managers and update tools; these do the actual installation and de-installation. Some have GUI front ends and some are command line. some will work with many package formats and some specialise. Some (more or less) rely on having a reasonable net connection to perform convenient updates and additions.
Usually, if you choose a distro that will chose the preferred package format for you (and may be one of the important factors in your choice of distro). Pretty much all of the debian-derived distros (& there are quite a few) are .deb distros, and for these you will have a choice of synaptic, adept, kpackage, etc. as the gui tools. For the Red Hat derived ones (and there are quite a few RH 'clones') and SuSE, you'll have YUM and Yast, but you can also use the rpm command from the command line.
You could also use Smart which is format-agnostic if you wanted, but, offhand, I can't think of anything that uses smart by default.
Gentoo and portage is a bit different; originally at least, Gentoo complied all the packages in place, rather than downloading pre-compiled packages. These days, gentoo has retreated a bit from compiling absolutely all of the packages in place, but it was originally set up to automatically manage this process.