Largely, no one definition can be decided on in either area which perpetuates misunderstandings and a disconnect between readings, reports, and ultimately how the terms are used by businesses in terms of naming what specifically the communication they are engaging in affects. Establishing another set of definitions is not the intent of this post (although I will offer three simple operational understandings further down), the idea is to put forth a strategy for approaching each term so they can be appropriately differentiated from one another and purposefully applied.
Differentiating the Concepts/Terms
Businesses need to understand, for their own purposes, how their identity differs from their image, and then reputation to be able to study them and establish how their actions impact each. SO, this is paramount for businesses to take the time to establish and is an internal process.
I would argue that some understandings of the terms are better than others if you want to quantify them and measure the impact of various actions on each. However, if a business simply wants to have a set difference between the concepts to be able to plan their marketing action, then choosing a way to understand each following through with it is the best course of action. On the flip side, not running with any set idea of each is the worst possible move to make.
For a simple preliminary breakdown where research and measurement of each is not as important, identity can simply be understood as the way that a business sees itself in their mission, values, goals, and organizational culture. A business' image can be understood as that which they extend outward toward their various publics which encompasses their tone, message, and the way that they want to be perceived by their publics and audiences. This represents the elements that the business portrays in their communication. Reputation is then the way that the business is seen by their publics (over time). The 'over time' element is problematic for measurement but is helpful in simple differentiation.
For more information regarding business' identity, image, and reputation and how they impact PR and internet marketing, reach out to me directly at rbuddenhagen@webimax.com and @ryanwbudd.