Adobe After Effects/Premiere Pro question for knowledgeable users?

I have a very simple piece of software right now, Premiere Elements 8, and I've been messing around with that for a couple of years and it's now 2nd nature to use, so I'm considering upgrading to Premiere Pro. Thing is, Adobe also has the After Effects program, which I'm under the impression is a special effects program designed to give you the ability to make videos made using a program like Premiere Pro OR Premiere Elements look much better. If this is the case, how then is Premiere Pro more useful than Premiere Elements if I could theoretically just make a video in either then polish them up using Adobe After Effects, wouldn't the end result basically be the same?

I absolutely appreciate that Premiere Pro MUST be hugely superior to Premiere Elements (it's 10x the price so it can't not be) I'm just asking literally what the differences between either are which make Premiere Pro worth purchasing BEFORE After Effects taking into account I already have a very basic video making program which, I imagine, would be compatible with Adobe After Effects?

I'm presently under the impression that Premiere Pro supports a more comprehensive range of media types, has a superior layout, and a few other things I saw in a Youtube review, but what features really justify the price difference between the two programs?