There are many species of algae, when I was doing microbiology studies I had a text book dedicated solely to the algal species the Great Lakes.
There are over 800 species of Euglena algae alone.
Some such as cyanobacteria,(are really not, but thought of as algae),thrive in nutrient rich (polluted) environments, and some in what would be considered non-polluted ones, and there are those species that thrive more according to light intensity, than nutrient but "all" will use nutrients, and those available nutrients seem to dictate which algal species thrive, so not really conflicting, just many types, desired and undesired by the aquarist.
It's all about balance in aquariums, if a balance is off, you may get unwanted Cyanobacteria (slime algae).
Above a tank of mine that got an intensity of light that produced slime algae, I needed to encourage different microorganisms to compete with it, to lose it.
In a well balanced system, you may get a desired species, below
In the Cenote below, there were Molly species that reached outrageous sizes of over 7", eating algae (almost exclusively)
These Cenotes were nutrient poor (no detectable nitrate), but received intense sunlight.
At the moment, I am running an algae scrubber type sump(it sits in direct sun), the algae in the sumps thick, but hardly any in the tank proper, nutrients used up (I believe), by the heavy higher plants and light fish load, in comparison.
So far the tank water, has had undetectable nitrate.
When some algae gets too thick in the sump, I rip some out, and feed it to the cichlids.