What do you mean by a text id, a serial id, and a UID, exactly?
Issues have a "key" such as ABC-123. This key identifies the project in which the issue exists by specifying the project's key (ABC) as the first part of the issue key. The second part of the issue key is a number that is assigned sequentially based on issue creation starting from 1 within that project.
An issue's Issue Key will change if it is moved from one project to another.
Issues also have an Issue ID which is numeric only and, I believe, assigned sequentially based on issue creation across all projects.
An issue's Issue ID will never be changed and will remain with it no matter what project the issue is moved to.
The relationships between the issues and other information attached to the issue (like Attachments, or links, or people, or...) can cross reference the Issue ID and never have to be updated if the issue is moved from one project to another. At the same time, having the Issue Key can quickly tell you to which project the issue belongs.
You can ignore the "UID", it means "unique identifier", which in Jira, is a description of both the issue "key" and the issue's ID in the database, it's not a separate thing from those two.
Unless it is being mixed up with "UUID", which is a "universally unique identifier". There's an essay here, but it's probably not of any use (and certainly boring) once you realise you can say a Jira's base url + issue key/id is a UUID.
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