The goal of process writing is to teach people about a process. Think of it as a "how-to" manual. Most technical writing is a form of process writing. An example would be the suggestions you might find in your textbook about how to go about finding a good issue to write about:
- Look around you for ideas, situations in the world today, that interest you.
- Consider your own interests and points of curiosity about those situations. What questions do you have?
- Freewrite to see if your questions and those issues lead to any interesting questions (etc.)
This is an example of a (recommended) process to be successful at a particular type of writing (persuasive writing), but the list of steps defines a process.
Note that I have no need to categorize people, things, or concepts into groups to draw conclusions about them. That is the point of a classification essay (another form of expository writing).