I went to System -> Requests -> Priorities and created a new priority, deleted one and changed the order around. I put the priority field in my custom default screen that set up for create / edit. The values on the screen are "Important", "Minor", "Simple" and the Priorities in the Administration section are "Critical", "Major", "Minor", "Critical".
It sounds like one of your admins has added a custom field with a different list from the Admin section?
I'm not sure about your phrase "system -> requests -> Priorities" as the off-the-shelf English in Jira is "Administration -> Priorities", so I'm questioning my understanding of what you're doing. But the list in the Admin screen you've got is definitely the default list of Jira priorities. If you're not seeing that, then check the field names carefully - is it definitely the *system* priority field offering you a different list, or is it some other field (Resolution is the other configurable list, or you could add a custom field select list with totally different options)
Ok, what can you see when you do a quick search and include the priority in the issue navigator? Does that look correct for existing issues?
Then, what happens if you actually create an issue with one of the offered priorities, or edit an issue that has one of the old ones?
One other random thought - have you tried to "translate" the priorities?
Oh wow, I put in an English "translation" to the priorities as "boop" for everything and now I have "boop" options in my "system default priority field".
I should now mention I have the Jira English ** Language Pack.
I've added a "English (US)" translation for all options and everything is showing up properly.
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