A process in its most general form is a mechanism for transforming an input or set of inputs into an output or set of outputs by the application of a set of tools and techniques (as an example, a "drill a hole" process starts with a piece of wood [the Input], uses a drill [the Tool] and delivers: a piece of wood with a hole, plus sawdust [the Outputs]).
The whole subset of the project management body of knowledge addressed by PMI is translated into a number of processes (49 in all). A process can only belong to a single PG and a single KA.
In the PMI standards, the processes are grouped into five PGs under the mnemonic IPECC, which stands for:
The potential for confusion arises because, (apart from "controlling"); the names of the groups could also apply to life cycle phases. The confusion is compounded by the fact that PMI presents the concept of processes and PGs before describing KAs. This issue is explained in more detail later on in this paper.
Note however, that processes from the various PGs can be invoked in many phases, and IPECC repeats within each one of the phases. To be more precise, there are multiple, simultaneous, asynchronous IPECC cycles running within each phase (e.g., you may be identifying new risks, while executing a part of communication plan, while closing a procurement, etc.)