Industrial IoT simply is just a term used to define when IoT is implemented in an industrial and manufacturing environment.
Industry 4.0 is the term used to describe the move towards digitalisation which has led to the current trend of automation and data exchange in manufacturing technologies and industrial settings. This includes IoT, cloud computing and cyber-physical systems. Industry 4.0 will see shifts in Heavy Industry which will be heavily driven by IoT and Artificial Intelligence.
"The Industrial Internet provides a way to get better visibility and insight into the company's operations and assets through integration of machine sensors, middle ware, software, and back-end cloud compute and storage systems. Therefore, providing a solution of transforming business operational processes using the feedback from the results gained by interrogating large data sets through advanced analytics.
The business gains are achieved through operational efficiency gains and accelerated productivity, which results in reduced unplanned downtime and optimized efficiency and therefore profits."
(Source: Industry 4.0 by A Gilchrist)