At the gathering of the fantasy creatures, a small group of elemental beasts gathered at the bar.
"Oh, interesting!" said the cat, "if you remove two letters from your type, you have your name!"
"Wow, that's right," agreed the horse, "and it seems that if you remove three letters from your name, you are left with YOUR type!"
The bovine suddenly perked up - "Wow, I never even thought of it that way, but if I remove four letters from my type, I'm left with MY name!"
"And we never even had to rearrange the letters for any of them," the cat said.
What three elemental animals were chatting here?