When submitting a ticket to support, you will be asked to select a priority. Priority is lacking any definition - this is because the priority is whatever you and your organization define it as. The customer priority (shorted on the forms as priority) is Support's way of asking the impact or importance the ticket has to your organization and its needs (business, technical, etc.).
Issue severity will align with the definitions on this page. Support will ultimately determine the severity level for any issue.