ITIL defines a partial taxonomy in that it defines processes in two different ways, functions, organizations, and systems.  There is no apparent structure to their taxonomy and the conflicting use of the term process leads to confusion.

I contend that a clear structured taxonomy of terms is needed to make it easier for students to organize and comprehend the different parts of ITSM.

ITIL V3 defines system in its generic form:

A number of related things that work together to achieve an overall objective.

This means that we have systems of different types at all levels of any potential taxonomy.  I propose using the generic systems definition to organize our taxonomy as a taxonomy of systems.  In part I base this preference on Dr. Deming's work on systems.  Arguably, all modern quality improvement efforts stem at least in part from Dr. Deming's work in systems theory.  Further I believe, that the increasing complexity of Enterprise IT requires systems of management designed to deal with increased complexity, such as systems theory.  For these reasons and more I propose the use of the term system to define every classification in the taxonomy. 

Items that are named generically such as Incident Management would be labeled systems e.g. Incident Management System.  Some systems are very precicely defined and do not need to be followed by the term system e.g. process.  By definition process is a system of activities defined in a very precise way.  (ITIL uses a mismash of definitions to call its classifications processes when they do not fit the classical definition)

Process is defined in ITIL V3 as:

A structured set of Activities designed to accomplish a specific objective.  A process takes one or more defined inputs and turns them into defined outputs.  A process may include any of the roles, responsibilities, tools and management controls required to reliably deliver the outputs.  A process may define policies, standards, guidelines, activities, and work instructions if they are needed.

This definition sets up process as a catch all or generic term which would be fine if you never needed to map a process.  Further, this definition confuses the ITIL idea of functions with processes. (function - a team or group of people and the tools they use to carry out one or more processes or activities.)  Process mapping requires a much more rigorous definition that provides for precise repeatablity and consistency in diagramming. 

Alternatively to the ITIL definition I propose the following definitions:

”a structured, measured set of activities designed to produce a specific output for a particular customer or market. It implies a strong emphasis on how work is done within an organization, in contrast to a product focus’s emphasis on what. A process is thus a specific ordering of work activities across time and space, with a beginning and an end, and clearly defined inputs and outputs: a structure for action. ... Taking a process approach implies adopting the customer’s point of view. Processes are the structure by which an organization does what is necessary to produce value for its customers.”

Davenport (1993)

”a collection of activities that takes one or more kinds of input and creates an output that is of value to the customer.”

Hammer & Champy (1993)

”a business process is a series of steps designed to produce a product or service. Most processes (...) are cross-functional, spanning the ‘white space’ between the boxes on the organization chart. Some processes result in a product or service that is received by an organization's external customer. We call these primary processes. Other processes produce products that are invisible to the external customer but essential to the effective management of the business. We call these support processes.”

Rummler & Brache (1995)

”a set of linked activities that take an input and transform it to create an output. Ideally, the transformation that occurs in the process should add value to the input and create an output that is more useful and effective to the recipient either upstream or downstream.”

Johansson et al. (1993)

These definitions are much more precise and leave the resources out of the process which allows for effective mapping.