The shiny-server.conf file in /etc/shiny-server is the configuration file for Shiny Server and all its functionality. It is installed in the same location on all operating systems.
The other shiny-server.conf file controls the service, including startup and shutdown, and system-level controls including log levels. This file gets installed in a location determined by the initialization system on the environment. For instance, it is installed in /etc/init for systems that use Upstart to control the service, and in /etc/init.d for systems that use init.d. For systems that use systemd, this file is located in /etc/systemd/system and is called shiny-server.service. See the Shiny Server admin guide for more details.