What is the difference between Prority and Urgency - Are they not the same?

hi,
pleased to answer to you about this subtle distinction :
First point :
Depending on the opinion or the position occupied by each, a ticket can be qualified as urgent or not.
Just as well, the notion of priority may differ among staff members.
Second point:
Moreover, there is no real connection between those two notions, even though an urgency is often a priority. In the same way, something of priority often becomes urgent.
But, in fact, one not necessarily induces the other. And even less when the judgments diverge from several people.
Conclusion:
The description of the ticket indicates, gives a first information to the resource which will treat it according to its degree of urgency or not, or even blocking (and therefore rather urgent). Generally, the urgency concerns the good end of the project or the application itself. The priority is the ticket processing order to handle these good ends.
Priority is given to the processing of tickets including a notion of added value on the interest of processing this ticket before and after others, taking into account, of course, the declared level of urgency.
In short, urgency is not a priority even if it sometimes contributes to it. The priority is a second sort order that takes into account or not the urgency or not of this ticket.
For example, URGENT and HIGH PRIORITY should be handled first, NOT URGENT with AVERAGE PRIORITY can be processed before the URGENT ticket with LOW PRIORITY. It depends on both, the priority given first and then the urgency as an indicator.

To make it short : urgency is defined by requestor (on description part) and priority is defined by responsible (on treatment part) depending on criticality of ticket.

Since the actual documentation is in GitHub, it's too complex for me to edit.

Our reporsitory is not on Github but on sourceforge.
There may be Github forks, they are not official ones.

So if I send you the page URIs and the distilled text that needs to be inserted in specific paragraphs, would it be ok?

Yes, but take care to start from ourt latest version to avoid conflicts