Are you asking for the zoa type too?
It's some kind of favia, kinda like my unknown one at home.
Anyways, that doesn't look like a ball anemone at all, i have some and they're nothing close to that.
Those appear to be tentacles, some sort of small coral.
it's causing your zoas to close, it might be stinging it. I would break and chip that piece off and keep an eye