Question: Is there a UML diagram to visually show the processes in a system?
Yes, you can use use case diagrams to represent the use cases (processes) in a software system. Use case diagrams show the actors in a system, and the ways in which these actors use the system.
This is why I use the terms "use cases" and "processes" interchangeably. IMHO, "use case" is a fancy way of saying "process", or perhaps more accurately, user-initiated processes, or event-driven processes.