Football Manager Classic is a new mode introduced in Football Manager 2013 as a less time consuming way to play Football Manager. It is still Football Manager, you will jus find that a number of responsibilities have been taken over by your backroom staff or have disappeared completely.
For example, you, the manager, will still take control of training but it will only be at 'full team' level only - there is no individual player training. There are also no Team Talks or Opposition Reports as the key here is to get you into the match as quickly as possible.
Matches are played out in a 'Highlights Only' fashion. There is also the option of just choosing 'Instant Result' and skipping the entire match if you are in a real hurry.