A journey can also be described as a series of steps, designed to achieve a particular outcome.
A process is predictable, pre-defined, repeatable and mechanical.
A journey is adventurous, undefined, surprising, unique and organic.
A process is generally defined and imposed by one person, to be performed by someone else.
A journey is generally undertaken by a person for his or her own reasons.
I would love to see business adopt a journey metaphor instead of a process metaphor, when describing what we do around here.