Story Mode is the first mode of play you get when you enter a level, and the only option you have when first entering the stage. Here, the game gives you characters based on your current scenario, and the game follows the story of the movie you're currently playing.
When in Story Mode, you will notice that you cannot access some areas as the characters you are given cannot use abilities to get to said areas. This is when you return in Free Play, where you can use any character you've unlocked. In Story Mode you can get some Mini-Kit canisters, however you cannot get all of them. (With some exceptions, which I'll get to soon.) Again, this is where Free Play comes in.
There is also a True Jedi Meter, this can be obtained in either Story or Free Play (Although I suggest doing it in Story. As the amount needed in Free Play is always higher.) To obtain this you need to collect a certain amount of studs, which are those little single pronged coins you find scattered on the ground, or in objects you can destroy. In this game they aren't too difficult (With a couple exceptions.) and getting all 17 will unlock the bonus level for play.
In this game, and this game only. Vehicle stages can only be played in Story Mode. This means you CAN get all 10 Canisters in the stage. I will however, still be listing the canisters for the stage in a Free Play guide. Just note that there is no Free Play for Vehicle stages.
The guides are listed below, with each Episode page leading to that movies levels. When you begin the game you only have access to Episode I, after beating Negotiations, you can then return to Dexter's Diner and play Episode II or III.