There are 3 methods cross platform saves, cross platform multiplayer and remote play.
Cross platform saves : 2 separate games, one for vita one for ps3. You move the save between consoles to continue. Example ruin/warriors lair and MLB 2012.
Cross platform multiplayer : 2 separate games, one for vita one for ps3. In this case a person playing a multiplayer game can play against someone else playing the game on ps3. Wipeout and hustle kings are examples.
Remote play : game runs on ps3 but instead of using a tv for view and dual shock 3 for control, the vita is used via a wifi connection. Very little support for this now, just psone games, pixel junk.
Sharing dlc. Across platform is separate from these and up to publisher to allow or not, but it is more likely to occur with cross platform save and multiplayer games to allow the cross play functions to work.
Rotor.
