Mostly, Companies are using Corel or Illustrator and what's the reason of using one of these mostly?

because it a vector graphics software. whether it is a small file or large file the raw quality of it is very fine, it's good in web graphics shows high quality print media creating website using illustrator by copying it's css and paste it on edge code you can create a beautiful and responsive website.. 

I think it was for popularity and convergencies. The both mentioned software is well used, well knowned so talent seeker won't find any difficulties to find experts who use it to work for their companies. Also it is installed on many computer, people easily send files between companies/computer without any difficulties to open it or edit the files later, except for difference between software version of course.

ILLUSTRATOR !!  BUT SOME COMPANIES USING COREL LIKE PRINTS INDUSTRY