Is the same JVM used by all Java applications running or, does 'one JVM per Java application' apply? (say the applications are IntelliJ IDEA, a server and NetBeans for example)
Further, is there any connection between JVMs assigned and processes used by each Java application?
Generally speaking, each application will get its own JVM instance and its own OS-level process and each JVM instance is independent of each other.
There are some implementation details such as Class Data Sharing, where multiple JVM instances might share some data/memory but those have no user-visible effect to the applications (except for improved startup time, hopefully).
A common scenario however is a single application server (or "web server") such as Glassfish or Tomcat running multiple web applications. In this case, multiple web applications can share a JVM.