Illustrator is sort of like Photoshop in the sense that GFX can be made with it, but as a licensed Adobe user here's where popular vs intended use comes in.
The term "Photoshop" (e.g. to photoshop) has become so popular that it is the go to program for things like sigs and creating graphic media from scratch. That's not what it was ​meant​ to do, per se. Photoshop is meant to clean up already created Photos, and perhaps even express yourself artistically on them (being the reason they include brushes and other such tools and features). Since it became the flag runner program, they imported nearly all of the features in the other graphic media suites to Photoshop, which nearly overrules the need to even use Illustrator.
Illustrator, on the other hand, is necessary for seasoned professionals in the realm of art. Most people use it in combination with some sort of capacitive touch screen to get the most from the program. It is really geared more for creating things from scratch (which like I said, Photoshop has the ability to do, to an extent). To wrap it up, Illustrator is meant for hand-drawn and paintings done on a digital apparatus, and is more suitable for creations like sprites, comics, cartoons, etc. Photoshop can also be used, but when it comes to those "little things" that artists need to separate the mice from the men in their art, Illustrator is the way to go.
Adobe After Effects is a program that allows you to add SFX to a video (eg light sabers, or someones head getting blown up). It is also popular for creations like video bumpers. Not a program that's very necessary to own only because there are so many templates and ready-to-use bumpers purchasable online for low prices, in my opinion.
