Platinum and below can change tag categories when it’s used on less than 50 posts. For Builders to Moderators, it’s less than 1,000 posts. Only Admins can change tag categories without limit.
If you think a tag needs a category change and you’re unable to change it, you can submit a BUR for it. It is usually best to use BURs when changing categories of large tags even if you can do it yourself.
The prefixes are art: for artist tags, char: for character tags, copy: for copyright tags, gen: for general tags, and meta: for meta tags. Note that new tags are general by default, as you have seen.