"Canon Endings" are the endings you'll want to collect while working towards unlocking the True Ending. They are the "real" endings whereas the others are deemed "Possibilities of the Continuum Shift...". Below is a good link for earning each Canon Ending...
http://blazblue.wikia.com/wiki/BlazBlue:_Continuum_Shift/Sto...Refer to this guide as some choices, battle outcomes and even use of Distortion Drives can affect the outcomes. It's strongly suggested that when you're using characters you aren't familiar with you use beginner mode. It makes relatively effective combos fairly easy, allowing you to breeze through Story Mode.