The difference is PC is the only one that wants to be at this particular school. The others are looking for their best gig with no allegiance to this school. Morris obviously knows that PC would rather make $175k here than $225k in Waco or someplace.
"Big Joe" sounds like context or just a description used by Galloway after he mentions in the previous sentence in that article of him being 6-4, 280 to describe the size of Greene, but I do not believe anyone else called him that. I have not seen or heard of it any other time.
You and others are correct in that the nickname "Mean Green" is in reference to the play of our defense back then and not specifically a nickname of Joe Greene then.
Here is one version of the Mean Green nickname origin from Randy Cummings, DRC...
Here is another variation of how the Mean Green nickname evolved...
Our brand is growing, Mean Green Nation. We are spending unprecedented amounts on our football program, as well as our department in general.
We have one of the best coaches in our school history leading our basketball program.
Eric Morris is going to lead our football program to new heights. Coach O and Co are going to put our footprint on the DFW high school recruiting market. We will no longer be ignored or unknown in the nations best resource for football talent.
Jared Mosely, the perfect AD for us, has been hired and will be leading us into the top G5 conference in the land.
Why do I bring all of this up? We need to be passionate as ever about 1) Getting our history right, and 2) Getting our name right. Tell people about Big Joe, not just Mean Joe. Stomp your foot (adult like), look people in the eye, and explain to them that it has been 30+ years since we were called North Texas State and it's about damn time they stopped calling us that.
The time is now. Love y'all. Go Mean Green.