There are a lot of differences between cyanobacteria and green algae. Cyanobacteria are prokaryotic micro-organisms; this means they are organisms who do not have nucleus or any other organelles in their cells. While green algae are eukaryotic organisms, that is, they are organisms which have nucleus and other organelles in their cells. Cyanobacteria are always considered to be dangerous to their environment, there presence is harmful to other microorganisms around. While green is less harmful.
One thing to notice about cyanobacteria is that, they reproduce only by asexual means of reproduction and they also produce their own food through photosynthesis. Green algae, on the other hand, also manufacture their own through photosynthesis, but they reproduce by both sexual and sexual means of reproduction. Cyanobacteria have always been considered to contain some toxic substances which are harmful to other organisms around their habitat, but green algae have some nutritional values to most of the green plant.