it looks like a Palythoa, they are very common in tidal pools and mostly ignored by aquarists, due to its ugly appearance. This particular variant is even less desirable, as it releases a lot of mucus.
In some places it is called "cow slobber" because of that.
It is also worth mentioning they carry one the strongest poison known to men (palitoxin) and their collection is illegal in the largest part of our coast.
why does the large specimen say "real, fake"? They could be palys or zoas, but they kind of also look like acans. it may just be my eyes (which are meant to be wearing glasses atm), it's hard to tell with the distance/colour/etc... did you ever figure it out conclusively? or have better pics?