It's different than "running the app" because a web application isn't simply run--it's run in the context of the container. A command-line
Java application is run--it has no dependencies other than the JVM (and any external libraries it uses). A web application relies on the container to feed it requests, determine the application's context, and so on.
When you deploy a web application the container figures out how to route requests to the application, initializes the application, and so on.