What the difference between premiere pro and after effects with examples of their capabilities?

premiere pro is a montage program , so you can cut unwanted scenes , make color correction , make transition, chroma key, and collect or your scenes to have the final movie at the end. So premiere pro is a montage software for video editing 

After effects is a software can do VFX , motion graphics , some video editing for short scenes , it can remove chroma too and you can make some character animation and use expressions to make awesome effects for your video. 

finally, what we do ?

first you collect or your scene at premiere pro to edit it and export it to after effects to make some effects and animation for it 

After effects is compositing software and  premiere pro is video editing software.