The demarcation is the requirement of context for a coach.  Generally speaking if a coach requires context (asks the client for more information), they are engaged in single loop learning or the performance against a standard without a shift in governing variables.  I call it problem solving.

If process is involved, then the coach is not concerned with context but the "way" or manner in which the person is arriving at conclusions. [ Ladder of Inference ]  This "way" or "process" is independent yet interrelated with context, however learning through a process is different than learning through a context.

In context, we must align with the appropriate understanding of it in order to "interject" and be helpful in most cases (remaining in context).  This produces the "what" that is in question.  This process indeed can be seen as a process by those who use context as the driver, however, the difference usually lies (between single and double loop learning) in the shift of the underlying values or governing variables.

In regards to process, we enable the functioning of decision-making through "how" we arrive at conclusions.  Most of the time, this will require a shift in the underlying values or governing variables as the "current" modus operandi, or process we use for drawing conclusions is governed by a set of underlying values or variables (mental models).  Therefore, the reason we're coming up with the set of issues is due to these governing variables being out of alignment or insufficient in terms of complexity to resolve the "problem" created at this level.  Yet, how we make decisions is separate from the context.  Merely asking how to do something doesn't necessarily cause us to arrive at the how of the process.

Memory & Learning

In the above discussion, context requires memory and process requires learning, or unmemorizing.  If I might be so bold as to suggest that to the extent that memory plays a role, it blocks the movement from the current "problem state" to the future "solution" state due to its hold on the governing variables that exist to cause the problem state--in memory.

[As a side note, there is never arrival as each solution state sets in motion the creation of additional problem states.  Often these are much more complex than the previous problem states which were satisfied by the current governing variables.]

So, let me finish to the point

As I think about coaching and which direction I want to move towards, I gravitate towards process, as it allows me to focus on something that applies across disciplines, rather than trying to "memorize" all the things I need to know to function effectively in context.  E.G. "how do I coach a person who....

I do believe both are necessary as you will get distinct advantages from either.  My tendency is to feel that contextual coaching requires a degree of expertise and experience within the context at a variety of complex levels.  The closer the match and alignment between what the client wants and needs and what the coach has to offer is critical in my view and thus will constitute the effectiveness of the arrangement. [This postulate is also consistent with developmental stage theory as well]

On the other hand, process expertise will apply to a broader set of domains and in some cases, be applicable to "context" driven sets of problem states.  Yet, substituting process work when contextual work is required within a set of governing variables will be less effective. [Requirements of skill where no shift in underlying variables is required, such as how to change a "lathe" position.]

The "real" issue becomes--what is the cause of the problem state.  It could be either context or process and sometimes both.  A contextual coach will fail most of the time to identify the "cause" of the problem if it is outside of context because of the failure to understand precisely the process that one uses to arrive at decisions.

In some cases, I speculate that process work will require more integration, flexibility and systems knowledge, except of course when the context is integration, flexibility and systems knowledge--an interesting paradox to be sure!