That white stuff isn't hair algae. I get it too and suck it up with a turkey baster if I don't get it all out during water changes. The algae that does grow on my walls and decore is a light-dark green. I notice it's dark green if it's further away from my light and light green if it's closer to it. That is what hair algae does based on what I've read.
He is an article about hair algae
since I thought about fighting it at first. Now I just let it grow and scrub it off when it starts to spread too much. I'm still trying to figure out the exact identity of the floating white stuff, but I personally think it's Brown Algae
since I know my light is crappy. I wouldn't be surprised if it did start to look more brown under a light that is more than decorative.
When I have the money I am going to upgrade the bulb to see if that second stuff is really algae. If it doesn't then I'll read up on it more. If I'm wrong, the link about brown algae also summarizes other types of algae. I hope it helps. :)