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.