In various parts of the books, ITIL refers to "Functions" rather than "Processes". For instance, Incident Management is introduced as a process and Facilities Management as a function. So, what is the difference?
ITIL Functions and Processes: Definition and Examples
By definition, a 'Function' is an organizational entity, typically characterized by a special area of knowledge or experience. Examples would be a team operating the SAP environment, a software development department, or - to name a function outside of the IT organization - a Human Resources (HR) department. ITIL 'Processes', in contrast, are clusters of activities which produce a defined outcome, like the ITIL Incident Management process.
Several functions may have a part in a process (the Service Desk and the SAP operating team might both have to perform activities within the Incident Management process).
Much confusion stems from the fact that in the real world there are often "Functions" and "Processes" with identical names: For example, the Facilities Management team (a "Function") will perform a set of facilities-related activities, which as a whole are called the Facilities Management process.
Functions and Processes in an ITIL Process Model
In a process model like the ITIL Process Map, the challenge is to represent activities performed by functions as well as information flows involving functions (for example, inputs provided by Application Management to other processes). Most process modeling notations - like BPMN  (Business Process Model and Notation) - readily allow to model information flows between processes, but offer no obvious guidance on how to model such flows between processes and functions.
The ITIL Process Map therefore implements the ITIL functions as "ad-hoc  processes in order to be able to show complete information flows to and from those functions.
As a result, the ITIL Process Map features a Facilities Management process even though, strictly speaking, the ITIL books define Facilities Management as a function. This also applies to IT Operations Control, Application Management, and Technical Management.
 Source: Business Process Model and Notation (BPMN) version 2.0 - Specification, as of January 2011: www.omg.org/spec/BPMN/2.0 and BPMN_20_spec.pdf
 As per BPMN, "ad-hoc" processes "do not contain a complete, structured BPMN diagram description from start event to end event [... and] may also contain data objects and data associations."
By: Andrea Kempter , IT Process Maps.
ITIL Functions and Processes: Definition > Functions and Processes in an ITIL Process Model