I will keep this short and sweet. An upgrade of a client for example is moving from 2012 to SP1 or R2. An update is installing a cumulative update (cu1, cu2, etc).
To automatically upgrade your clients, in the console go to \Administration\Overview\Site Configuration\Sites
Then at the top click on Hierarchy Settings > Automatic Client Upgrade > then enable the setting.
To update your clients, see the following blog post for details on how to find the updates in your console, distribute them, and deploy them. Please note this will include updates for the console, server, and clients. You will first have to install the CU hotfix on the server.
For an updated list of the various SCCM 2012 versions – see this blog post.