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...