After Effects & Premiere

Question

After Effects n00b here. Seeking to learn and improve. But at the outset of my journey I have some confusion, already.
Just like Illustrator and InDesign have functionality overlap, so do After Effects and Premiere. So, I ask:
How do they compliment each other? How does one decide to designate certain tasks for one or the other, when they both handle video and animation?

Answer 1

> You can "create motion graphics, apply visual effects, composite visual elements, perform color correction," etc in Premiere. Can you not???
Not easily or well. (Actually, the color correction tools in Premiere Pro are coming along, so that one might be a "yes".)
> but marketing verbiage aside, I'm really seeking the experience-based thoughts and opinions of my peers - the ones who actually use the software professionally, day-in day-out.
That's not "marketing verbiage"; that's a summary of the applications written by someone who has been using both full-time for about 10 years now (me, as it happens, since a long time ago I wrote the After Effects documentation).
Here's another way of answering the question:
Use Premiere Pro to take movies, cut them apart into shorter pieces, and arrange them in time.
Use After Effects to layer many pieces of movies and other animated images (created in After Effects or imported from elsewhere) on top of each other to create composite images.
Premiere Pro is optimized for arranging movies in time. After Effects is optimized for changing the way movies look.
Each has many rudimentary features of the other, but trying to edit a movie in After Effects or create motion graphics in Premiere Pro is bound to leave you frustrated.