Except for paid apps as tachyons has pointed out (which can be installed and uninstalled with apt-get but only once purchased in the Software Center), the Software Center is primarily a front end for the various apt- commands--not just apt-get. For example, the Software Center will also search for packages and let you edit your Software Sources.

The main practical distinction between the two is that the Software Center will automatically fetch information about what packages are available from where and in what versions. In contrast, when installing or upgrading software with apt-get, you should run sudo apt-get update first if you haven't done so recently. sudo apt-get install ... does not (ever) cause sudo apt-get update to be run automatically (though it may be run automatically up to once a day as part of automatic updates in the system).