Algae photosynthesizes, has chlorophyll and other coloring matter.
No, algae is not really white. It may look black, grey, red, yellow or almost any shade of green, but it will always look some sort of color.
Fungi live off other living things, and do not make their own food from sunlight and simple elements. Fungi are often white, but can be almost any color. Not too often green, though, and their coloring materials are not photosynthetic.
Blob of goo with white dots is pond snail eggs. I would remove this as fast as you find it.