They are carpet anemones (Stichodactyla tapetum). They generally come in a ton of different colors, are fairly hardy compared to other carpets, reproduce very quickly, can be manually divided (I ripped one in half by accident and it survived without any problems), and are truly a carpet anemone in regards to how sticky they are and how much they can take down. They are known to grab fish that wander into their grasp including those that are much larger than they are. Once they shoot their nematocysts, not much a fish can do to get away unless it's much larger than the anemone.
There is also the maxi mini which is a larger variant of the mini-carpets, I believe the same genus and species, but it gets much larger (about the same size as a rock or flower anemone) and to my knowledge is much more difficult to manually divide. The maxi minis sometimes have better coloration, although I'm not sure if this is simply because you can see the colors better. I have minis and they have some great coloration with greens, pinks, purples, and whites splashed throughout, but when they are expanded you rarely see anything but the purple and pink, which to my eye, means pretty much grey...