If I have two shots of the same frame, but one frame is with a character and the other is without one,
how is AE can distinguish between the two so I can apply an effect of the character "appearing" from no-where?
AE doesn't distinguish, you tell AE what to do. Generally this effect is done with a cut, sometimes hidden with a flash, puff of smoke, lens flare. Create a new composition, and add both your layers and offset them in time where you want your character to enter the scene and add any effects to cover up the cut if you that's what you want.
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.