Are these the other sponges you are seeing? If so, the common name for them is q-tip or pineapple sponges. Harmless filter feeders that come and go. The worst thing I've seen with some types of sponges is a rare case where they smother a small patch of zoas. Here's a pic of pineapples...
I would call them stiff, but flexible. I took some tweezers and tied one in a knot once to see if it would die but it didnt. You pretty much need to "kill" the rock to get rid of them. They are a pain!