A management initiative intends to change of capability, whereas a process repeatedly cycles through similar tasks to produce a result. An online site says that a process is “a sequence of activities that take an input and produce an output. In business, a process is supposed to add value to the input before producing the output.” For law departments, a process is the fundamental unit of activity that needs to be managed; it describes how the department produces value.
Two examples should illustrate the difference between and initiative (or program) and a process. When you set up a pro bono program it is an initiative; thereafter, when you take on a new pro bono matter and handle it, you are in a process. To address the long-term filing needs of the legal department by research into alternative solutions, investment and implementation is an initiative; thereafter to file the red-wells of a particular matter or to bar code documents is part of a process.
This definition is leaky, I agree, because a management initiative, such as to increase diversity, is not likely ever to end, and thus partakes of a characteristic of a process (See my post of Oct.17, 2006 on processes and their tools.).