TOMCAT_HOME is partly my fault. There is no such thing as TOMCAT_HOME. There are actually two environment variables here: CATALINA_HOME and CATALINA_BASE. But I can never remember which is which, so I cheat and just say "TOMCAT_HOME".
Tomcat is split into 2 parts. One part is common to all instances of Tomcat. It contains things like the bin and lib directories.
The other part is replicated per-instance. It contains the work, temp and log directories. And conf, which is where the server.xml that defines what ports a given Tomcat instance uses.
So to run (and start/stop) multiple Tomcat instances, you no longer have CATALINA_HOME and CATALINA_BASE aimed at the same "TOMCAT_HOME" directory, but instead you have one CATALINA_HOME for all the Tomcats and a separate CATALINA_BASE for each Tomcat.
An IDE is no substitute for an Intelligent Developer.