Caulerpa in both photos, different types. As for getting rid of them, I don't have good advice. I tried for years in a past set up without real success, they grow rapidly and will regrow from roots that are next to impossible to manually remove. Are you able to remove those two rocks to clean outside the tank?
The right is Caulerpa, I've had both of those in my tank. It's actually why I neglected my tanks for so long it almost defeated me. It's caused by excessive nutrients like all algae. I have a 75G and as I mentioned in another thread earlier my LFS let me bring some in and drop a little in each tank they had a Foxface in. I bought the Foxface that showed the most interest in it and he ate it all in a few months. Then I had a nitrate problem since the algae wasn't there to absorb it. So while the Foxface fixed the symptoms of the problem, the main problem was still there. I solved it with a Sulfate denitrator. There's a lot of different ways to treat excess nutrients in the water. Would need more details about your setup.
You can remove them from the rock by pulling them off I find tweezers work well to pull the roots and small parts of the algae that want to stay attached. You are almost certain to miss a tiny piece and notice when it starts to grow back but just remove again after a few attempts you should be able to get it off the rocks
Confirmed- Sea grape caulerpa which Tangs would mow down like candy. Simply detach at the threads which it use to cling to rock by pulling it off sthread by thread and place in sump or discard.
Your LFS might even take it for a little store credit
I guess I will try to manually remove it with tweezers for now and if fail nuke the rock... its a pity cause I have a few coral growing on the live rock nicely...
I have used hydrogen peroxide with a toothbrush to strategically focus on uglies without soaking the whole rock. If rock is integrated into aquascape, then use toothbrush underwater with frequent soaking toothbrush with H202 and scrubbing rock. This works on Aptasia as well.
I have 2 tanks, a 90 and a 50. My 50 is infested with this. I've been pulling it out and throwing in the 90 where it's eaten a bit by a yellow tang and also by emerald crabs and hermit crabs. I'm going to get more crabs for the 50.