What is the difference of corporate image and corporate identity?

ooooh that is a difficult one i think its on the client view that your working with 

DO you think that the graphic designer can do corporate identity?

Corporate image is something how the general public and your consumer perceive your company while corporate identity is what the company wants it to be perceived. There's a lot of aspects that go in making a corporate identity like logo, brochure designing, corporate policy, etc. Corporate identity is a more proactive activity indulged in by the company while corporate image is entirely based on the user experience and how they feel about the company.