Factory automation is what we say an industrial automation. Industrial automation means all types of automation done in industry. Industrial automation is the complete automation of the entire process done an industry where there is least human intervention in process, apart from that the only job a human does in monitoring and controlling the whole automation via SCADA or DCS.
Process automation is a kind of Factory automation because process industry is a kind of industry. Process industry is the one related with refineries, paper and pulp, petrochemical, etc. Because they have tendentiously more PID control processes than any other industry. This is why it’s called process automation.
There are conceptual differences between factory automation and process automation.