App Manager isn't really a store-like thing as such, it is a *user-friendly* GUI for the apt-get package manager. It lets you choose a package to install, figures out what dependencies that package has, and assuming they exist in the repositories you have enabled, installs (or un-installs) it all for you. The same thing can be done on the command line using apt-get.

The store is something new, and is an unfamiliar concept to us regular Linux users.