Logo design is a subset of Corporate Identity design.
A company’s corporate identity includes the following:
1. Logo design
2. Brand colors
3. Brand name
4. Stationery including the letterhead, business card, envelope, memo and other stationery items like writing pads etc.
5. Appearance of the company’s identification marks on various media – on mugs, diaries, video, print, web etc. – a usage guide for example.
6. Any other design deliverables related to the identity of the whole company for example powerpoint presentations.
An organization might already have a logo in place but not have a comprehensive corporate identity. A logo design usually contains two elements: the logo shape and the typeface/font used for the name of the company/brand, whereas corporate identity includes a whole gamut of identification marks / colors / themes and presentation for the company.