Kintypes that involve species of your own creation can be considered otherkin or fictionkin, depending on your presence and who you’re talking to.
But otherkin also sometimes seems to be only for Earth animals and not fantasy-based creatures. Could you clear this up?
This is actually a bit backwards. Therian is the term that’s pretty much just for earth animals. Otherkin is specifically for fantasy creatures such as elves, unicorns, griffons, etc.