Everything is working now. Thanks for your help. Per your question, I revisited my installation process. There were several websites that I was using as guidance to navigate the Linux, Java, Minecraft, Forge, and mod installations. It did become a bit confusing and I combined some of the instructions. When I went back though the process, I realized that I did not need the Minecraft server to run Forge, AND I also realized that the mods were not back compatible. The 1.12 versions only worked with the 1.12 version of Minecraft. This is probably something that a seasoned Minecraft player knows inherently, but it was news to me.
So for anyone who is trying to set up a Linux Minecraft server without much history with Minecraft these are the steps that I took to get mine to work:
1) Install Linux OS (Ubuntu)
2) Install Java (OpenJDK)
3) Install Linux text editor and functions
4) Download and install Forge Server in different directory
5) Run java -jar forge-x.xx.x-installer.jar --installServer in Forge directory
6) Run bash run.sh in Forge directory
7) Accept the EULA by editing the false to true
8. Add mods with the target version of Minecraft to the mods folder in the Forge directory
9) Run bash run.sh in Forge directory
The Forger server should initiate with an indication in the status messages that the mods in the mods folder have been recognized. Then a GUI with utilization metrics will launch. The server is running at this point.
The client should have Java and the mods installed in their mods folder. Launch the client Minecraft application and it should work with the mods installed.
Happy gaming!