Logo Design: A logo is the graphic symbol that represents a person, company or organization. If the logo is well-known enough, such as the Nike swoosh, you may even see a logo used without the name of the business that it is associated with. Normally, most marks have a typographic part that more clearly spells out the name of the organization. A logo can also be purely typographic. It is called a logotype or wordmark when only the letters of the name make up to the logo (there is no additional symbol). A great example is Coca-Cola’s red scripty type.
Brand Identity: Once a logo has been designed it gets applied to many different applications. These can be as simple as the logo placed in the top center of a piece of paper and calling it letterhead. When a brand identity really works, you should be able to recognize the brand even if you don’t see the logo. For example, Netflix’s red envelope is a simple yet powerful example of a brand identity.