On our JIRA Cloud implementation, we have three administration groups: site-admin, jira-administrator and administrator. What is the difference between jira-administrator and administrator?
So a jira-administrator is a user with JIRA Administrator and JIRA System Administrator permissions and an administrator only has the JIRA Administrator permission. But I thought the JIRA System Administrator permission group is not accessible in JIRA Cloud instances, and this means that it doesn't really make a difference which is which. I am not sure I understand how this works!
The most helpful page I've found on this topic is https://confluence.atlassian.com/cloud/manage-groups-744721627.html, which discusses the default groups for Cloud.
To answer the original question, it seems that the administrators and jira-administrators groups are equivalent for Jira Cloud. The administrators group seems to only be useful if you also have Confluence Cloud.
The site-admin group has additional permissions around user management and billing.
The other answer links to Jira Server documentation which talks about Jira System Administrators, which just confuses the issue if you ask me! (To be fair, the page I link to may not have existed when the question was asked, so perhaps the other answer had the best information available at the time...)
You've understood it correctly. It is possible to add and rename groups, and you could easily set up your system so that the JIRA admins belong to a group called "Banana" instead of "JIRA administrator". Or have multiple groups with admin access.
As you say, the Cloud system does not let anyone but Atlassian have system administrator, so my best guess is that you have added another "administrator" group for some other reason. Some add-ons will do things like that when they are installed too.
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