You don't "run" JSPs. JSPs are resources within webapps. You can deploy the same webapp (WAR or EAR) file to multiple servers, but if you are intending to work with multiple servers (Tomcat or otherwise) and a single copy of a WAR, you'll have to obey certain restrictions.
People commonly use "exploded" WARs with Tomcat. If you just take a WAR file and drop it into Tomcat's webapps directory, Tomcat will automatically explode it by default. You should not attempt to share that exploded copy, each Tomcat instance needs its own CATALINA_BASE, and that means it has its own distinct webapps directory.
To literally share the exact same WAR between multiple Tomcats, you need to define a deployment descriptor that points to a codeBase WAR that's external to all Tomcat instances. For example, a build directory in your Eclipse project.
Starting multiple Tomcats from Eclipse is a whole different issue. Most Tomcat control plugins are designed with the idea that one Tomcat is enough, even if you have multiple webapp instances to debug. So to start the second Tomcat, you would have to launch it manually and connect to it via the Remote Debugging facilities. Embedded Tomcat uses Remote Debugging as well, but the Eclipse Tomcat plugin will automatically handle that one.
An IDE is no substitute for an Intelligent Developer.