There may be one Java installation - library, etc. but each time you start a Java program it gets its own jvm instance. There may be shared library components but that is managed by the operating system.
Instead of running two Tomcat instances, it's possible to have a single instance listen on two different ports, thereby still having just a single server process. Not sure if that would help in your circumstances. For that you'd need additional Connector elements inside the Service element in your server.xml. See http://tomcat.apache.org/tomcat-5.5-doc/config/index.html for more details.