Some type of algae?

Hi all, hope I picked the correct forum for this type of problem. I have some type of (I assume) algae growing in now both of my 10g tanks. I dont know exactly how to describe it, but here goes. It seems to grow in patches on solid objects in the tank. It consists of green 'shoots' almost like hair, sometimes getting in excess of an inch or so. It tends to gather on top of the objects but I have seen it along the sides of driftwood and such. I have found large patches on top of lilly leaves. When I pull it out, it feels fairly 'stuck' to the object, but removal is not overly difficult and it comes out in patches again.

Once out of the water, it almost reminds me of a seaweed in the color and it has a rough texture to it. I dont believe I have seen any algae described quite like this so I thought it would be good to run it by here. The algae destroyer liquid I have (probably snake oil more than anything, I know...) doesnt do anything to control it.

The first time I ever noticed this, it was growing on top of a patch of java moss. for a short time, I thought this WAS java moss. It seems to attach to the slower growing plants most.

How can I get rid of this? Soaking my solid objects (substrate, non-live decorations) in bleach or something to that extent IS an option, however what to do with live plants?

Thanks in advance for reading through this post and for responses and I hope I was clear enough.

however rosy barbs probably get too large for a 10 gallon tank. What other fish may be good options?