Really vaguely worded question but in my mind, process is all the piping directly associated with chemical feeds, process side of heat exchangers, etc. Whatever your "process" is - stuff handling the raw materials, intermediate components/materials, and final components are "process".
"Utility" is everything else that supports the process work. Chilled water, river water, steam, nitrogen, air, etc...You need these for the process/equipment to work but they aren't process lines.