Is there a way, that an Eclipse launch configuration exists only in one mode? Either Run -or Debugmode. Until this point, I've only seen this mirror behaviour, that if I create a launch configuration in the Run Configurations menu (in Eclipse), it will also be created in the Debug Configurations menu.
The short answer is yes. Look at the debug configuration for "Remote Java Application". It isn't available in run mode.
The supported modes of the launch configurations are defined by the plug-ins with launch configuration type extension points. See Adding launchers to the platform