I am a student who is going for internship soon. However, I am not sure what I would want to do. I'm slightly better at Photoshop than Illustrator. However, there are only 2 jobs available for me. They are Graphic illustrator and Photography. I want to become a Advertiser when I am older however I am confused on which one to take.
It would serve you best to read the full job description and talk to both employers to make sure your skills would be the best fit.
Photoshop is probably the easiest of the programs to use, but it would be best especially in the illustrator position to know how to use Illustrator. Personally, out of InDesign, Illustrator and Photoshop, I actually use Photoshop the least, not that it's not important.
Each program has its qualities, but I mainly use Photoshop specifically for picture editing or anything that is rasterized. Illustrating in Photoshop can create massive files which can be a problem when trying to transfer files or when there's limited memory available.
My suggestion would be for you to go through illustrator tutorials. There are numerous sites and videos to help you with the basics and build up from there. My favorite (though it does cost something) is Lynda.com.
You will be best served over the life of your career by knowing both Photoshop and Illustrator.
For immediate needs, generally Photoshop knowledge can be slightly more useful out of the gate. But you won't go wrong by learning either.
And be aware, merely because an employment position is listed as "Photography" or "Illustration" that does not mean the other application won't be used.